Neural Ordinary Differential Equations

2018/06/19 by Ricky T. Q. Chen, Chen, Ricky T. Q., Yulia Rubanova +5 · 5 voices · 978 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Black box #Computational Physics and Python Applications #Computer science #Constant (computer programming) #Construct (python library) #Continuous modelling #Differential (mechanical device) #Differential equation #Generative Adversarial Networks and Image Synthesis #Latent variable #Mathematical analysis #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Ode #Ordinary differential equation #Residual #Sequence (biology) #Solver #Variable (mathematics) #cs.AI #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1806.07366

published in arXiv (Cornell University) 31, 6572-6583 (Cornell University)

openalex publication_date 2018/06/19 · arxiv created 2019/12/14 · arxiv updated 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

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• PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation
• Time-adaptive HénonNets for separable Hamiltonian systems
• Staying on the Manifold: Geometry-Aware Noise Injection
• Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization
• Metriplectic Conditional Flow Matching for Dissipative Dynamics
• Looped Transformers with Source-Centered State Evolution
• Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network
• Persistent Gaussian Perturbations Prevent Oversmoothing in Recurrent Graph Neural Networks
• Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework
• ODEWorld: A Continuous Predictive Architecture via Physical-Time Flow
• Physics-constrained neural ordinary differential equation models to discover and predict microbial community dynamics
• Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
• Efficient Explicit Taylor ODE Integrators with Symbolic-Numeric Computing
• Linear Power System Modeling and Analysis Across Wide Operating Ranges: A Hierarchical Neural State-Space Equation Approach
• Prompt-Guided Dual Latent Steering for Inversion Problems
• MTM: A Multi-Scale Token Mixing Transformer for Irregular Multivariate Time Series Classification
• Preconditioned Deformation Grids
• Breaking the Discretization Barrier of Continuous Physics Simulation Learning
• Emergent Topology of Optimal Networks for Synchrony
• Dynamic Gene Regulatory Network Inference with Interpretable, Biophysically-Motivated Neural ODEs
• Preference Trajectory Modeling via Flow Matching for Sequential Recommendation
• ViTCAE: ViT-based Class-conditioned Autoencoder
• Time-adaptive SympNets for separable Hamiltonian systems
• Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equations
• TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification
• Quantum neural ordinary and partial differential equations
• MeanFlowSE: one-step generative speech enhancement via conditional mean flow
• FlowCast-ODE: Continuous Hourly Weather Forecasting with Dynamic Flow Matching and ODE Solver
• Evidential Physics-Informed Neural Networks for Scientific Discovery
• CDFlow: Generative Gradient Flows for Configuration Space Distance Fields via Neural ODEs
• Floating-Body Hydrodynamic Neural Networks
• Spatiotemporal graph neural process for reconstruction, extrapolation, and classification of cardiac trajectories
• Reversible Deep Equilibrium Models
• Universal differential equations for systems biology: Current state and open problems
• Path Integral Sampler: a stochastic control approach for sampling
• Deep Convolutional Networks as shallow Gaussian Processes
• Learning non-Markovian Dynamical Systems with Signature-based Encoders
• C3DE: Causal-Aware Collaborative Neural Controlled Differential Equation for Long-Term Urban Crowd Flow Prediction
• Zero to Autonomy in Real-Time: Online Adaptation of Dynamics in Unstructured Environments
• Gradients, parallelism, and variance of quantum estimates
• Competitive Inner-Imaging Squeeze and Excitation for Residual Network
• Two ways to knowledge?
• Flow Straight and Fast in Hilbert Space: Functional Rectified Flow
• KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework
• SciML Agents: Write the Solver, Not the Solution
• The Hidden Width of Deep ResNets: Tight Error Bounds and Phase Diagram
• Uncertainty Propagation Networks for Neural Ordinary Differential Equations
• Sig-DEG for Distillation: Making Diffusion Models Faster and Lighter
• Improving Video Diffusion Transformer Training by Multi-Feature Fusion and Alignment from Self-Supervised Vision Encoders
• SAFT: Shape and Appearance of Fabrics from Template via Differentiable Physical Simulations from Monocular Video
• LatentVoiceGrad: Nonparallel Voice Conversion with Latent Diffusion/Flow-Matching Models
• OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case
• Unstructured to structured: geometric multigrid on complex geometries via domain remapping
• AI LLM Proof of Self-Consciousness and User-Specific Attractors
• BULL-ODE: Bullwhip Learning with Neural ODEs and Universal Differential Equations under Stochastic Demand
• Physics-Informed Neural Networks in Clean Combustion: A Pathway to Sustainable Aerospace Propulsion
• An Agentic AI Workflow to Simplify Parameter Estimation of Complex Differential Equation Systems
• Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data
• Quantum Filtering and Stabilization of Dissipative Quantum Systems via Augmented Neural Ordinary Differential Equations
• Data-driven discovery of dynamical models in biology
• A High-order Backpropagation Algorithm for Neural Stochastic Differential Equation Model
• Diffusion Secant Alignment for Score-Based Density Ratio Estimation
• Neuro-Spectral Architectures for Causal Physics-Informed Networks
• STL-based Optimization of Biomolecular Neural Networks for Regression and Control
• Echo State Networks as State-Space Models: A Systems Perspective
• Error analysis for learning the time-stepping operator of evolutionary PDEs
• Balancing Signal and Variance: Adaptive Offline RL Post-Training for VLA Flow Models
• An invertible generative model for forward and inverse problems
• Neural Architecture Search via Bregman Iterations
• Energy-Weighted Flow Matching: Unlocking Continuous Normalizing Flows for Efficient and Scalable Boltzmann Sampling
• Distribution estimation via Flow Matching with Lipschitz guarantees
• Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Space
• Exploring accuracy and uncertainty quantification in physics-informed neural networks for inferring microbial community dynamics
• Augmented KRnet for density estimation and approximation
• Discrete Noise Inversion for Next-scale Autoregressive Text-based Image Editing
• Preconditioned Regularized Wasserstein Proximal Sampling
• Learning Longitudinal Stress Dynamics from Irregular Self-Reports via Time Embeddings
• HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks
• Continuous Graph Neural Networks
• Cross-Domain Few-Shot Segmentation via Ordinary Differential Equations over Time Intervals
• Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models
• Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching
• Universal Representation of Generalized Convex Functions and their Gradients
• Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements
• FNODE: Flow-Matching for data-driven simulation of constrained multibody systems
• Generative Latent Space Dynamics of Electron Density
• OptMark: Robust Multi-bit Diffusion Watermarking via Inference Time Optimization
• Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning
• Studying Effective String Theory using deep generative models
• Self-composing neural operators for high-frequency and multiscale PDE surrogates
• Flowing Straighter with Conditional Flow Matching for Accurate Speech Enhancement
• Neural Field Turing Machine: A Differentiable Spatial Computer
• Objective Value Change and Shape-Based Accelerated Optimization for the Neural Network Approximation
• FlowMalTrans: Unsupervised Binary Code Translation for Malware Detection Using Flow-Adapter Architecture
• Data-Augmented Few-Shot Neural Emulator for Computer-Model System Identification
• Kolmogorov-Arnold Representation for Symplectic Learning: Advancing Hamiltonian Neural Networks
• STDiff: A State Transition Diffusion Framework for Time Series Imputation in Industrial Systems
• Energy-Based Flow Matching for Generating 3D Molecular Structure
• Generalization Bound for a General Class of Neural Ordinary Differential Equations
• From Prediction to Simulation: AlphaFold 3 as a Differentiable Framework for Structural Biology
• Amortized Sampling with Transferable Normalizing Flows
• Provable Mixed-Noise Learning with Flow-Matching
• Incorporating Pre-trained Diffusion Models in Solving the Schrödinger Bridge Problem
• Sesame: Opening the door to protein pockets
• Lorentz-Equivariance without Limitations
• On Scalable and Efficient Computation of Large Scale Optimal Transport
• Counterfactual Probabilistic Diffusion with Expert Models
• A Tutorial on Deep Latent Variable Models of Natural Language
• Distribution Matching via Generalized Consistency Models
• Cosmology-informed Neural Networks to infer dark energy equation-of-state
• Robust Convolution Neural ODEs via Contractivity-promoting regularization
• Learning State-Space Models of Dynamic Systems from Arbitrary Data using Joint Embedding Predictive Architectures
• Observable Optimization for Precision Theory: Machine Learning Energy Correlators
• Starobinsky in Stereo: SKA-CMB Synergy in SBI
• Forecasting Black Sigatoka Infection Risks with Latent Neural ODEs
• GeoMAE: Masking Representation Learning for Spatio-Temporal Graph Forecasting with Missing Values
• Implicit Hypergraph Neural Networks: A Stable Framework for Higher-Order Relational Learning with Provable Guarantees
• Real-time forecasting of chaotic dynamics from sparse data and autoencoders
• Identifying efficient routes to laminarization: an optimization approach
• Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)
• A Generalized Multinodal Model for Plasma Particle and Energy Transport
• Momentum Point-Perplexity Mechanics in Large Language Models
• When and how can inexact generative models still sample from the data manifold?
• Intrinsic training dynamics of deep neural networks
• Neural Bridge Processes
• FlowSE: Flow Matching-based Speech Enhancement
• Structure-Preserving Digital Twins via Conditional Neural Whitney Forms
• Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria
• A Stage-Aware Mixture of Experts Framework for Neurodegenerative Disease Progression Modelling
• Artificial intelligence in mitotic checkpoint modeling: transforming our understanding of cellular division through machine learning and predictive biology
• Learning geometries beyond asymptotic AdS
• Machine Learning-Based Nonlinear Nudging for Chaotic Dynamical Systems
• How and Why: Taming Flow Matching for Unsupervised Anomaly Detection and Localization
• Estimating Musical Surprisal from Audio in Autoregressive Diffusion Model Noise Spaces
• TANGO: Graph Neural Dynamics via Learned Energy and Tangential Flows
• Optimality Principles and Neural Ordinary Differential Equations-based Process Modeling for Distributed Control
• Multi-Marginal Stochastic Flow Matching for High-Dimensional Snapshot Data at Irregular Time Points
• Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems
• Lie Transform--based Neural Networks for Dynamics Simulation and\n Learning
• Variety Is the Spice of Life: Detecting Misinformation with Dynamic Environmental Representations
• SCFlow: Implicitly Learning Style and Content Disentanglement with Flow Models
• How Diffusion Prior Landscapes Shape the Posterior in Blind Deconvolution
• REFLECT: Rectified Flows for Efficient Brain Anomaly Correction Transport
• Physics-Embedded Neural ODEs for Sim2Real Edge Digital Twins of Hybrid Power Electronics Systems
• DeepKoopFormer: A Koopman Enhanced Transformer Based Architecture for Time Series Forecasting
• Diffusion models for inverse problems
• Epi²-Net: Advancing Epidemic Dynamics Forecasting with Physics-Inspired Neural Networks
• Revitalizing Canonical Pre-Alignment for Irregular Multivariate Time Series Forecasting
• Instance-Dependent Continuous-Time Reinforcement Learning via Maximum Likelihood Estimation
• CTBench: Cryptocurrency Time Series Generation Benchmark
• Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvements
• VFP: Variational Flow-Matching Policy for Multi-Modal Robot Manipulation
• The Vanishing Gradient Problem for Stiff Neural Differential Equations
• Unified Generation-Refinement Planning: Bridging Guided Flow Matching and Sampling-Based MPC for Social Navigation
• Flow Matching for Probabilistic Learning of Dynamical Systems from Missing or Noisy Data
• Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics
• WeightFlow: Learning Stochastic Dynamics via Evolving Weight of Neural Network
• Unlocking New Paths for Science with Extreme-Mass-Ratio Inspirals: Machine Learning-Enhanced MCMC for Accurate Parameter Inversion
• TrajSurv: Learning Continuous Latent Trajectories from Electronic Health Records for Trustworthy Survival Prediction
• Stability-Constrained AC Optimal Power Flow--A Gaussian Process-Based Approach
• GeoHNNs: Geometric Hamiltonian Neural Networks
• Forecasting chaotic dynamic using hybrid system
• Image-Guided Shape-from-Template Using Mesh Inextensibility Constraints
• Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks
• Weighted Conditional Flow Matching
• Learning Simulatable Models of Cloth with Spatially-varying Constitutive Properties
• Numerical PDE solvers outperform neural PDE solvers
• Explicit and Effectively Symmetric Runge-Kutta Methods
• An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations
• Why Flow Matching is Particle Swarm Optimization?
• Physics-Informed Learning of Proprietary Inverter Models for Grid Dynamic Studies
• Sparse Equation Matching: A Derivative-Free Learning for General-Order Dynamical Systems
• Augmenting Neural Differential Equations to Model Unknown Dynamical Systems with Incomplete State Information
• MedSymmFlow: Bridging Generative Modeling and Classification in Medical Imaging through Symmetrical Flow Matching
• Neural Ordinary Differential Equations for Learning and Extrapolating System Dynamics Across Bifurcations
• Physics-Informed Regression: Parameter Estimation in Parameter-Linear Nonlinear Dynamic Models
• Flow Stochastic Segmentation Networks
• STR-GODEs: Spatial-Temporal-Ridership Graph ODEs for Metro Ridership Prediction
• LagNetViP: A Lagrangian Neural Network for Video Prediction
• Reconstructing a dynamical system and forecasting time series by self-consistent deep learning
• Deep Learning-based Time-varying Channel Estimation for RIS Assisted Communication
• Beyond Silicon: Materials, Mechanisms, and Methods for Physical Neural Computing
• YuriiFormer: A Suite of Nesterov-Accelerated Transformers
• Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network
• Flow Matching Meets Biology and Life Science: A Survey
• A Physics-Augmented Machine Learning Constitutive Model for Damage in Solids
• Higher Gauge Flow Models
• Comparing Behavioural Cloning and Reinforcement Learning for Spacecraft Guidance and Control Networks
• Controllable Video Generation: A Survey
• Gauge Flow Models
• Momentum Multi-Marginal Schrödinger Bridge Matching
• Quantum Machine Learning in Multi-Qubit Phase-Space Part I: Foundations
• Geometrization of deep networks for the interpretability of deep learning systems
• Dynamics of a data-driven low-dimensional model of Rayleigh-Benard convection
• Neural Functions for Learning Periodic Signal
• STAGED: A Multi-Agent Neural Network for Learning Cellular Interaction Dynamics
• Matrix Lie Maps and Neural Networks for Solving Differential Equations
• A research framework for writing differentiable PDE discretizations in JAX
• Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis
• Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model
• GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transport
• Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling
• Small Data Explainer -- The impact of small data methods in everyday life
• Flow matching for reaction pathway generation
• Flows and Diffusions on the Neural Manifold
• A Generalizable Physics-Enhanced State Space Model for Long-Term Dynamics Forecasting in Complex Environments
• FD-Net with Auxiliary Time Steps: Fast Prediction of PDEs using Hessian-Free Trust-Region Methods
• G-Sim: Generative Simulations with Large Language Models and Gradient-Free Calibration
• Sensitivity Analysis of Transport and Radiation in NeuralPlasmaODE for ITER Burning Plasmas
• Intention-Conditioned Flow Occupancy Models
• Optimizing External Sources for Controlled Burning Plasma in Tokamaks with Neural Ordinary Differential Equations
• Modeling Partially Observed Nonlinear Dynamical Systems and Efficient Data Assimilation via Discrete-Time Conditional Gaussian Koopman Network
• Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learning
• Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching
• PINN-Obs: Physics-Informed Neural Network-Based Observer for Nonlinear Dynamical Systems
• Understanding Malware Propagation Dynamics through Scientific Machine Learning
• SILVA Networks as Structured Implicit Layers and Vector Attractors via Dynamic Interaction Fields
• Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time
• A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations
• Neural Network-Based Parameter Estimation for Non-Autonomous Differential Equations with Discontinuous Signals
• KPFlow: An Operator Perspective on Dynamic Collapse Under Gradient Descent Training of Recurrent Networks
• Remember Past, Anticipate Future: Learning Continual Multimodal Misinformation Detectors
• A Dynamical Systems Perspective on the Analysis of Neural Networks
• Implicit Machine Learning Force Fields Accelerate Molecular Dynamics Simulations
• Guarantees on Dynamical System Distinguishability for LLM Token Generation
• When do World Models Successfully Learn Dynamical Systems?
• A cautionary tale of model misspecification and identifiability
• Machine Learning in Acoustics: A Review and Open-Source Repository
• Differentiable Approximations for Distance Queries
• Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions
• First Contact: Data-driven Friction-Stir Process Control
• GEM: Group Enhanced Model for Learning Dynamical Control Systems
• Time Resolution Independent Operator Learning
• Energy-Based Transformers are Scalable Learners and Thinkers
• Characterizing control between interacting subsystems with deep Jacobian estimation
• Consistency of Learned Sparse Grid Quadrature Rules using NeuralODEs
• Physics-Embedded Neural ODEs for Learning Antagonistic Pneumatic Artificial Muscle Dynamics
• BoltzNCE: Learning Likelihoods for Boltzmann Generation with Stochastic Interpolants and Noise Contrastive Estimation
• Stable Differentiable Modal Synthesis for Learning Nonlinear Dynamics
• Physics-Informed Neural ODEs for Temporal Dynamics Modeling in Cardiac T1 Mapping
• Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flows
• Minimally dissipative multi-bit logical operations
• Multi-Model Framework for Reconstructing Gamma-Ray Burst Light Curves
• Fully data-driven inverse hyperelasticity with hyper-network neural ODE fields
• Towards foundational LiDAR world models with efficient latent flow matching
• TuCo: Measuring the Contribution of Fine-Tuning to Individual Responses of LLMs
• Flow-Modulated Scoring for Semantic-Aware Knowledge Graph Completion
• Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks
• Spatiotemporal Local Propagation
• D2C: Diffusion-Denoising Models for Few-shot Conditional Generation
• 3D Shape Generation: A Survey
• Adjoint Schrödinger Bridge Sampler
• Unfolding Generative Flows with Koopman Operators: Fast and Interpretable Sampling
• Neural Function Modules with Sparse Arguments: A Dynamic Approach to Integrating Information across Layers
• Hybrid Generative Modeling for Incomplete Physics: Deep Grey-Box Meets Optimal Transport
• rodeo: Probabilistic Methods of Parameter Inference for Ordinary Differential Equations
• CaloHadronic: a diffusion model for the generation of hadronic showers
• ResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computers
• Distilling Normalizing Flows
• A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
• Control and optimization for Neural Partial Differential Equations in Supervised Learning
• Permutation Equivariant Neural Controlled Differential Equations for Dynamic Graph Representation Learning
• Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control
• Operator Forces For Coarse-Grained Molecular Dynamics
• ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized partial differential equations from sparse and noisy data
• Simulation-Free Differential Dynamics through Neural Conservation Laws
• DDOT: A Derivative-directed Dual-decoder Ordinary Differential Equation Transformer for Dynamic System Modeling
• Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics
• IndexTTS2: A Breakthrough in Emotionally Expressive and Duration-Controlled Auto-Regressive Zero-Shot Text-to-Speech
• Efficient many-jet event generation with Flow Matching
• Controlled Generation with Equivariant Variational Flow Matching
• Geometric Contact Flows: Contactomorphisms for Dynamics and Control
• Reversing Flow for Image Restoration
• Mesh-Informed Neural Operator : A Transformer Generative Approach
• Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotion
• Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities
• Optimal Navigation in Microfluidics via the Optimization of a Discrete Loss
• T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders
• Time-dependent density estimation using binary classifiers
• Minimizing Structural Vibrations via Guided Flow Matching Design Optimization
• MIRA: Medical Time Series Foundation Model for Real-World Health Data
• The Catechol Benchmark: Time-series Solvent Selection Data for Few-shot Machine Learning
• Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
• A Survey of Physics-Informed AI for Complex Urban Systems
• Generalizing to New Dynamical Systems via Frequency Domain Adaptation
• NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regions
• Stable CDE Autoencoders with Acuity Regularization for Offline Reinforcement Learning in Sepsis Treatment
• DiffusionBlocks: Block-wise Neural Network Training via Diffusion Interpretation
• Differentiable Simulation of Hard Contacts with Soft Gradients for Learning and Control
• On Interpretability of Artificial Neural Networks: A Survey
• Bures-Wasserstein Flow Matching for Graph Generation
• SeqPE: Transformer with Sequential Position Encoding
• Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
• Towards Robust ResNet: A Small Step but A Giant Leap
• Flow-Based Policy for Online Reinforcement Learning
• GGBall: Graph Generative Model on Poincaré Ball
• Learning to Integrate
• Audio synthesizer inversion in symmetric parameter spaces with approximately equivariant flow matching
• Quantum-Inspired Differentiable Integral Neural Networks (QIDINNs): A Feynman-Based Architecture for Continuous Learning Over Streaming Data
• RollingQ: Reviving the Cooperation Dynamics in Multimodal Transformer
• Transient Dynamics in Lattices of Differentiating Ring Oscillators
• A detailed and comprehensive account of fractional Physics-Informed Neural Networks: From implementation to efficiency
• Symmetrical Flow Matching: Unified Image Generation, Segmentation, and Classification with Score-Based Generative Models
• History-Aware Neural Operator: Robust Data-Driven Constitutive Modeling of Path-Dependent Materials
• Efficiency Robustness of Dynamic Deep Learning Systems
• Identifiability Challenges in Sparse Linear Ordinary Differential Equations
• STARFlow: Scaling Latent Normalizing Flows for High-resolution Image Synthesis
• Transformative or Conservative? Conservation laws for ResNets and Transformers
• FlexSpeech: Towards Stable, Controllable and Expressive Text-to-Speech
• Simulating Fokker-Planck equations via mean field control of score-based normalizing flows
• RNE: plug-and-play diffusion inference-time control and energy-based training
• FuseUNet: A Multi-Scale Feature Fusion Method for U-like Networks
• EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulator
• Exponential Family Variational Flow Matching for Tabular Data Generation
• Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics
• Contrastive Flow Matching
• Aligning Latent Spaces with Flow Priors
• ODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting
• Feature-Based Lie Group Transformer for Real-World Applications
• Progressive Tempering Sampler with Diffusion
• On Fitting Flow Models with Large Sinkhorn Couplings
• Learning long range dependencies through time reversal symmetry breaking
• Neural Jumps for Option Pricing
• Neural MJD: Neural Non-Stationary Merton Jump Diffusion for Time Series Prediction
• Riemannian Denoising Diffusion Probabilistic Models
• Nature's Insight: A Novel Framework and Comprehensive Analysis of Agentic Reasoning Through the Lens of Neuroscience
• BrisT1D Dataset: Young Adults with Type 1 Diabetes in the UK using Smartwatches
• Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equations
• STRGCN: Capturing Asynchronous Spatio-Temporal Dependencies for Irregular Multivariate Time Series Forecasting
• Online Adaptation of Terrain-Aware Dynamics for Planning in Unstructured Environments
• Large deviations for scaled families of Schrödinger bridges with reflection
• Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
• Efficient Training of Physics-enhanced Neural ODEs via Direct Collocation and Nonlinear Programming
• Bridging Neural ODE and ResNet: A Formal Error Bound for Safety Verification
• Conformer-based End-to-end Speech Recognition With Rotary Position Embedding
• Learning Optical Flow Field via Neural Ordinary Differential Equation
• Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme
• FDSG: Forecasting Dynamic Scene Graphs
• Latent Stochastic Interpolants
• SPOT-Trip: Dual-Preference Driven Out-of-Town Trip Recommendation
• Efficient Regression-Based Training of Normalizing Flows for Boltzmann Generators
• Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs
• Weight-Space Linear Recurrent Neural Networks
• Rhythm Controllable and Efficient Zero-Shot Voice Conversion via Shortcut Flow Matching
• CoVoMix2: Advancing Zero-Shot Dialogue Generation with Fully Non-Autoregressive Flow Matching
• Real-Time Person Image Synthesis Using a Flow Matching Model
• A condensing approach to multiple shooting neural ordinary differential equation
• PointODE: Lightweight Point Cloud Learning with Neural Ordinary Differential Equations on Edge
• Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fields
• TumorGen: Boundary-Aware Tumor-Mask Synthesis with Rectified Flow Matching
• Optimization of Module Transferability in Single Image Super-Resolution: Universality Assessment and Cycle Residual Blocks
• Aligning Protein Conformation Ensemble Generation with Physical Feedback
• HD-NDEs: Neural Differential Equations for Hallucination Detection in LLMs
• Ergodic Generative Flows
• Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations
• A Data-Driven Method for Modeling Creep-Fatigue Stress-Strain Behavior Using Neural ODEs
• Efficiently Access Diffusion Fisher: Within the Outer Product Span Space
• Trajectory Generator Matching for Time Series
• Advanced Binary Neural Network for Single Image Super Resolution
• JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows
• Physics-Infused Reduced-Order Modeling for Analysis of Multi-Layered Hypersonic Thermal Protection Systems
• IMTS is Worth Time × Channel Patches: Visual Masked Autoencoders for Irregular Multivariate Time Series Prediction
• Navigating the Latent Space Dynamics of Neural Models
• A comprehensive analysis of PINNs: Variants, Applications, and Challenges
• Accelerating Optimization via Differentiable Stopping Time
• Streaming Flow Policy: Simplifying diffusion/flow-matching policies by treating action trajectories as flow trajectories
• Predicting the Dynamics of Complex System via Multiscale Diffusion Autoencoder
• ReinFlow: Fine-tuning Flow Matching Policy with Online Reinforcement Learning
• Causal Posterior Estimation
• Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models
• Multitemporal Latent Dynamical Framework for Hyperspectral Images Unmixing
• multivariateGPT: a decoder-only transformer for multivariate categorical and numeric data
• Continuous-Time Attention: PDE-Guided Mechanisms for Long-Sequence Transformers
• LeDiFlow: Learned Distribution-guided Flow Matching to Accelerate Image Generation
• Developing hybrid mechanistic and data-driven personalized prediction models for platelet dynamics
• ParticleGS: Learning Neural Gaussian Particle Dynamics from Videos for Prior-free Physical Motion Extrapolation
• Graph Wave Networks
• PCDCNet: A Surrogate Model for Air Quality Forecasting with Physical-Chemical Dynamics and Constraints
• Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures
• Rotary Masked Autoencoders are Versatile Learners
• On the Relation between Rectified Flows and Optimal Transport
• Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints
• Gradient Flow Matching for Learning Update Dynamics in Neural Network Training
• Graph Element Networks: adaptive, structured computation and memory
• Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics
• Velocity-Inferred Hamiltonian Neural Networks: Learning Energy-Conserving Dynamics from Position-Only Data
• FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation
• Continuous Normalizing Flows for Uncertainty-Aware Human Pose Estimation
• Automatic and Structure-Aware Sparsification of Hybrid Neural ODEs
• SuperMAN: Interpretable and Expressive Networks over Temporally Sparse Heterogeneous Data
• From Single Images to Motion Policies via Video-Generation Environment Representations
• Computational Inertia as a Conserved Quantity in Frictionless and Damped Learning Dynamics
• Latent Trajectory Dynamics in Large Language Models: A Manifold Evolution Framework with Empirical Validation
• PDPO: Parametric Density Path Optimization
• VORTA: Efficient Video Diffusion via Routing Sparse Attention
• How Particle System Theory Enhances Hypergraph Message Passing
• Hamiltonian Theory and Computation of Optimal Probability Density Control in High Dimensions
• KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches
• ExARNN: An Environment-Driven Adaptive RNN for Learning Non-Stationary Power Dynamics
• CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshots
• Flexible MOF Generation with Torsion-Aware Flow Matching
• TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation
• Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory
• Liouville PDE-based sliced-Wasserstein flow for fair regression
• FlowMixer: A Constrained Neural Architecture for Interpretable Spatiotemporal Forecasting
• A manifold-aware Neural ODE surrogate model for stochastic induction heating with anisotropic electrical conductivity
• Multivariate Latent Recalibration for Conditional Normalizing Flows
• Neural network based control of unknown nonlinear systems via contraction analysis
• Learning Continuous-Time Dynamics by Stochastic Differential Networks
• Monotonic Gaussian Process Flow
• Why and When Deep is Better than Shallow: Implementation-Agnostic State-Transition Model of Deep Learning
• Generative AI for Autonomous Driving: A Review
• Oh SnapMMD! Forecasting Stochastic Dynamics Beyond the Schrödinger Bridge's End
• Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers
• Sample and Computationally Efficient Continuous-Time Reinforcement Learning with General Function Approximation
• Adverseness vs. Equilibrium: Exploring Graph Adversarial Resilience through Dynamic Equilibrium
• Latent Flow Transformer
• Scalable Autoregressive 3D Molecule Generation
• Learning Spatio-Temporal Dynamics for Trajectory Recovery via Time-Aware Transformer
• Minimum-Excess-Work Guidance
• CacheFlow: Fast Human Motion Prediction by Cached Normalizing Flow
• Hamiltonian of polymatrix zero-sum games
• Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling
• FlowPure: Continuous Normalizing Flows for Adversarial Purification
• Sampling NNLO QCD phase space with normalizing flows
• Alternators With Noise Models
• Shallow Flow Matching for Coarse-to-Fine Text-to-Speech Synthesis
• Model alignment using inter-modal bridges
• Proximal optimal transport divergences
• Continuous Domain Generalization
• Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action
• EulerLoRA: Rank-Driven Jump Dynamics for Calibrated Parameter-Efficient Fine-Tuning
• S-Crescendo: A Nested Transformer Weaving Framework for Scalable Nonlinear System in S-Domain Representation
• Revisiting Residual Connections: Orthogonal Updates for Stable and Efficient Deep Networks
• Reformulating Neural Operators in d+1 Dimensions for Embedding Evolution
• MLLM-based Discovery of Intrinsic Coordinates and Governing Equations from High-Dimensional Data
• A parameterized Wasserstein Hamiltonian flow approach for solving the Schrödinger equation
• Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
• Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schrödinger Bridge
• CN101 - A Digital Thermodynamic Computer for Generative AI
• Regularity and Stability Properties of Selective SSMs with Discontinuous Gating
• The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations
• Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning
• Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning
• Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiency
• What's Inside Your Diffusion Model? A Score-Based Riemannian Metric to Explore the Data Manifold
• Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline
• Schrödinger Generator for High-Dimensional Integration and Sampling on Quantum Many-Body States
• Path Gradients after Flow Matching
• A Physics-Chemistry-Informed Neural Network (PCINN) for Real-Time Spatial-ALD Coverage Prediction and Reliable Kinetics Inversion
• Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators
• Controllability, Multiplexing, and Transfer Learning in Networks using Evolutionary Learning
• Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data
• Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations
• Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations
• Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era
• You Only Look One Step: Accelerating Backpropagation in Diffusion Sampling with Gradient Shortcuts
• IM-BERT: Enhancing Robustness of BERT through the Implicit Euler Method
• DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers
• Learning inelastic constitutive models from stress–strain data under hard thermodynamic constraints
• SPIN-ODE: Stiff Physics-Informed Neural ODE for Chemical Reaction Rate Estimation
• AI Approaches to Qualitative and Quantitative News Analytics on NATO Unity
• Over-the-Air ODE-Inspired Neural Network for Dual Task-Oriented Semantic Communications
• Physics-Assisted and Topology-Informed Deep Learning for Weather Prediction
• Accelerated Integration of Stiff Reactive Systems Using Gradient-Informed Autoencoder and Neural Ordinary Differential Equation
• Neural-network-based design and implementation of fast and robust quantum gates
• Learning the Simplest Neural ODE
• FlowDubber: Movie Dubbing with LLM-based Semantic-aware Learning and Flow Matching based Voice Enhancing
• Robust Deep Learning-Based Physical Layer Communications: Strategies and Approaches
• Distilling Two-Timed Flow Models by Separately Matching Initial and Terminal Velocities
• Learning and Transferring Physical Models through Derivatives
• Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings
• SynPAT: A System for Generating Synthetic Physical Theories with Data
• Wasserstein Policy Optimization
• Detecting Modeling Bias with Continuous Time Flow Models on Weak Lensing Maps
• ChargeFlow: Flow-Matching Refinement of Charge-Conditioned Electron Densities
• Unlocking the Potential of Linear Networks for Irregular Multivariate Time Series Forecasting
• Bullet Trains: Parallelizing Training of Temporally Precise Spiking Neural Networks
• PackFlow: Generative Molecular Crystal Structure Prediction via Reinforcement Learning Alignment
• Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers
• Dicovering the emergent nonlinear dynamics of acoustically levitated cube clusters
• JointDiT: Enhancing RGB-Depth Joint Modeling with Diffusion Transformers
• A Survey of Robotic Navigation and Manipulation with Physics Simulators in the Era of Embodied AI
• Simulation as Supervision: Mechanistic Pretraining for Scientific Discovery
• Reconstructing and forecasting disease trajectories of patients with Alzheimer's disease using routine data in resource-constrained settings
• Geometric Autoencoder for Diffusion Models
• On Geometry Regularization in Autoencoder Reduced-Order Models with Latent Neural ODE Dynamics
• A new architecture of high-order deep neural networks that learn martingales
• JFlow: Model-Independent Spherical Jeans Analysis using Equivariant Continuous Normalizing Flows
• Dynamical System Parameter Path Optimization using Persistent Homology
• From Lab to Wrist: Bridging Metabolic Monitoring and Consumer Wearables for Heart Rate and Oxygen Consumption Modeling
• Looped World Models
• Neuro-Symbolic ODE Discovery with Latent Grammar Flow
• Learning Topological Representations for Molecular Dynamics
• Strong Stochastic Flow Maps
• Zero-Flow Encoders
• Control Laws in Aging and Longevity: A Control Theory of Aging for Gerotherapeutic Drug Discovery
• PyCC.id: A package for hypothesis-driven equation discovery with structural identifiability
• ProT-GFDM: A Generative Fractional Diffusion Model for Protein Generation
• ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes
• Learning biophysical models of gene regulation with probability flow matching
• Functional Whole-Brain Models: A New Framework for Unifying Brain Structure and Cognitive Function
• End-to-end differentiable network traffic simulation with dynamic route choice
• The DIME Architecture: A Unified Operational Algorithm for Neural Representation, Dynamics, Control and Integration
• Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function
• DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction
• Learning Brenier Potentials with Convex Generative Adversarial Neural Networks
• Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control
• Integration Flow Models
• Flow Along the K-Amplitude for Generative Modeling
• Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations
• Imitation Learning for Autonomous Driving: Insights from Real-World Testing
• Introducing Interval Neural Networks for Uncertainty-Aware System Identification
• Foundation Inference Models for Ordinary Differential Equations
• Continuous Adversarial Flow Models
• Geometric structure of ideal data-driven dynamical model using RfR method
• ECLIPSE: A Composable Pipeline for Predicting ecDNA Formation, Evolution, and Therapeutic Vulnerabilities in Cancer
• Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization
• Retina gap junctions support the robust perception by warping neural representational geometries along the visual hierarchy
• Compressing Complexity: A Critical Synthesis of Structural, Analytical, and Data-Driven Dimensionality Reduction in Dynamical Networks
• Revisiting Reset Mechanisms in Spiking Neural Networks for Sequential Modeling: Specialized Discretization for Binary Activated RNN
• Plasma State Monitoring and Disruption Characterization using Multimodal VAEs
• Flow Matching Ergodic Coverage
• EvtGraph: Event-Adaptive Compression for Sparse Temporal Graph Learning in Multimodal Time Series
• Training Crossroads for Recurrent Vision Transformers: Recurrence, Neural ODEs, and Deep Supervision
• Deep convolutional neural networks for uncertainty propagation in random fields
• Estimation of Heat Transfer Coefficient in Heat Exchangers from closed-loop data using Neural Networks
• Language Models Are Implicitly Continuous
• Spacetime Neural Network for High Dimensional Quantum Dynamics
• Topological Schrödinger Bridge Matching
• Physics-informed reduced-order modelling with equivariant spectral submanifolds
• SJEPA: Learning Elegant Latent Dynamics with Hybrid Symbolic-Neural Predictors
• Neuromorphic Parameter Estimation for Power Converter Health Monitoring Using Spiking Neural Networks
• A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations
• Fast Online Adaptive Neural MPC via Meta-Learning
• Opt-ODENet: A Neural ODE Framework with Differentiable QP Layers for Safe and Stable Control Design (longer version)
• Universal differential equations for optimal control problems and its application on cancer therapy
• Learning Conditionally Independent Transformations using Normal Subgroups in Group Theory
• EclipseNETs: Learning Irregular Small Celestial Body Silhouettes
• Riemannian Neural Geodesic Interpolant
• Large models for machinery fault diagnosis: Current advances and future directions
• DiffAqua
• Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matching
• MoBGS: Motion Deblurring Dynamic 3D Gaussian Splatting for Blurry Monocular Video
• Uncertainty quantification of neural network models of evolving processes via Langevin sampling
• HyperFlow: Gradient-Free Emulation of Few-Shot Fine-Tuning
• Approximating High-Order Adversarial Attacks Using Runge-Kutta Methods
• Neural ODE to model and prognose thermoacoustic instability
• JANC: A cost-effective, differentiable compressible reacting flow solver featured with JAX-based adaptive mesh refinement
• MusFlow: Multimodal Music Generation via Conditional Flow Matching
• Robust Learning with Implicit Residual Networks
• Machine learning on neutron and x-ray scattering and spectroscopies
• RBM-Flow and D-Flow: Invertible Flows with Discrete Energy Base Spaces
• On the minimax optimality of Flow Matching through the connection to kernel density estimation
• Safe Physics-Informed Machine Learning for Dynamics and Control
• Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations
• Data Assimilation for Robust UQ Within Agent-Based Simulation on HPC Systems
• Federated Spectral Graph Transformers Meet Neural Ordinary Differential Equations for Non-IID Graphs
• A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems
• Dysarthria Normalization via Local Lie Group Transformations for Robust ASR
• Reasoning Errors Have a Region and a Direction in the Residual-Stream Trajectory of LLMs
• Curriculum Multiple Shooting for Robust Training of Neural and Universal Differential Equations
• Potential Matching Optimal Transport: Continuous Normalizing Flows for Exact p-Wasserstein Dynamics
• Hierarchical Flow Matching for 3D Point Cloud Generation
• A neural operator view on U-Nets for inverse imaging problems
• Multi-resolution Score-Based Variational Graphical Diffusion for Causal Disaster System Modeling and Inference
• Bi-PT: Bidirectional Cross-Attention Point Transformers for Four-Chamber Heart Reconstruction from Sparse Cardiac MRI Data
• Time Series Classification through Diffeomorphic Time Warping (DiffTW)
• FlowAdam: Implicit Regularization via Geometry-Aware Soft Momentum Injection
• The Pontryagin Maximum Principle for Training Convolutional Neural Networks
• Matrix effects in laser-induced breakdown spectroscopy: A review from fundamental mechanisms to data-driven modeling strategies
• DUE: A Deep Learning Framework and Library for Modeling Unknown Equations
• Debiasing 6-DOF IMU via Hierarchical Learning of Continuous Bias Dynamics
• Revisiting Likelihood-Based Out-of-Distribution Detection by Modeling Representations
• External-Wrench Estimation for Aerial Robots Exploiting a Learned Model
• A machine learning approach to fast thermal equilibration
• Neural Motion Simulator: Pushing the Limit of World Models in Reinforcement Learning
• Physics-informed Modularized Neural Network for Advanced Building Control by Deep Reinforcement Learning
• Biomechanical Constraints Assimilation in Deep-Learning Image Registration: Application to sliding and locally rigid deformations
• Structured Knowledge Accumulation: The Principle of Entropic Least Action in Forward-Only Neural Learning
• Conditioning Diffusions Using Malliavin Calculus
• Neural differential equation [wikipedia]
• Flow-based generative model [wikipedia]
• Adjoint state method [wikipedia]
• David Duvenaud [wikipedia]

Discussions

• Neural Ordinary Differential Equations [hn, 240 points, 60 comments]
• Neural Ordinary Differential Equations [lobsters, 10 points, 1 comments]
• Neural Ordinary Differential Equations [hn, 3 points, 0 comments]
• oh ya, that makes more sense. i really want to get back to this stuff. this paper would be so much fun to try implementing in julia (no idea what has happened in this space in the last 4-5 years) ar [bsky, 1 points, 1 comments]
• arxiv.org/abs/1806.07366 [bsky, 0 points, 0 comments]

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