1. Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
   2025/12/22 by Philipp L. Kinon, Kinon, Philipp L., Simon R. Eugster +3 · 1 citation
   Engineering · Mathematics · Physics and Astronomy · #Computational Engineering #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Finance #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Robotics (cs.RO) #Systems and Control (eess.SY) #and Science (cs.CE) #electronic engineering #information engineering
2. Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries
   2025/12/16 by Rowan, Conor, Hampleman, Kai, Maute, Kurt +1 · 1 citation
   Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
3. Error Analysis on a Novel Class of Exponential Integrators with Local Linear Extension Techniques for Highly Oscillatory ODEs
   2025/11/19 by Qi, Zhihao, Deng, Weibing, Zhu, Fuhai · 1 citation
   Mathematics · Computer Science · #Numerical methods for differential equations #Matrix Theory and Algorithms #Advanced Mathematical Modeling in Engineering
4. Self-adaptive weighting and sampling for physics-informed neural networks
   2025/11/07 by Wenqian Chen, Chen, Wenqian, Amanda A. Howard +3 · 3 citations
   Physics and Astronomy · Mathematics · Materials Science · #Model Reduction and Neural Networks #Numerical methods for differential equations #Machine Learning in Materials Science
5. Second-order discretization of Dyson series: iterative method, numerical analysis and applications in open quantum systems
   2025/10/17 by Zhenning Cai, Cai, Zhenning, Yixiao Sun +3 · 1 citation
   Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Quantum many-body systems
6. Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves
   2025/09/09 by Genming Bai, Bai, Genming, Harald Garcke +3 · 2 citations
   Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
7. High precision PINNs in unbounded domains: application to singularity formulation in PDEs
   2025/06/24 by Yixuan Wang, Ziming Liu, Wang, Yixuan +7 · 3 citations
   Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering
8. Error analysis of BDF schemes for the evolutionary incompressible Navier--Stokes equations
   2025/06/20 by García-Archilla, Bosco, John, V., Novo, Julia · 3 citations
   Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
9. 2N-storage Runge-Kutta methods: c-reflection symmetry and factorization of the Butcher tableau
   2025/06/10 by Alexei Bazavov, Bazavov, Alexei · 2 citations
   Mathematics · Computer Science · Engineering · #Numerical methods for differential equations #Matrix Theory and Algorithms #Electromagnetic Simulation and Numerical Methods
10. Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient
    2025/06/04 by Conor Rowan, Rowan, Conor, John A. Evans +5 · 5 citations
    Physics and Astronomy · Engineering · Mathematics · #Model Reduction and Neural Networks #Topology Optimization in Engineering #Numerical methods for differential equations
11. KerZOO: Kernel Function Informed Zeroth-Order Optimization for Accurate and Accelerated LLM Fine-Tuning
    2025/05/24 by Zhendong Mi, Qitao Tan, Mi, Zhendong +8 · 3 citations
    Engineering · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #I.2.6 #I.2.7 #Machine Learning (cs.LG) #Magnetic confinement fusion research #Nuclear reactor physics and engineering #Numerical methods for differential equations
12. Hierarchical dynamic domain decomposition for the multiscale Boltzmann equation
    2025/05/06 by Domenico Caparello, Caparello, Domenico, Lorenzo Pareschi +3 · 3 citations
    Engineering · Computer Science · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Numerical methods for differential equations
13. A residual weighted physics informed neural network for forward and inverse problems of reaction diffusion equations
    2025/04/09 by Krishna Murari, Pradip Roul, Murari, K. +3 · 1 citation
    Physics and Astronomy · Materials Science · Mathematics · #Model Reduction and Neural Networks #Machine Learning in Materials Science #Numerical methods for differential equations
14. A Two-Level Direct Solver for the Hierarchical Poincaré-Steklov Method
    2025/03/06 by Joseph Kump, Kump, Joseph, Anna Yesypenko +3 · 2 citations
    Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations
15. PhysicsSolver: Transformer-Enhanced Physics-Informed Neural Networks for Forward and Forecasting Problems in Partial Differential Equations
    2025/02/26 by Zhenyi Zhu, Yuchen Huang, Zhu, Zhenyi +3 · 3 citations
    Materials Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Machine Learning in Materials Science #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
16. S4S: Solving for a Diffusion Model Solver
    2025/02/24 by E. T. Frankel, Frankel, Eric, Sitan Chen +9 · 4 citations
    Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Numerical methods for differential equations
17. Sharp Phase Transitions in Estimation with Low-Degree Polynomials
    2025/02/20 by Youngtak Sohn, Alexander S. Wein, Sohn, Youngtak +1 · 7 citations
    Computer Science · Earth and Planetary Sciences · Mathematics · #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Geophysics and Gravity Measurements #Numerical methods for differential equations #Probability (math.PR) #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks
18. A posteriori error bounds for finite element approximations of steady-state mean field games
    2025/02/20 by Yohance A. P. Osborne, Osborne, Yohance A. P., Iain Smears +3 · 1 citation
    Engineering · Mathematics · Decision Sciences · #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #Probabilistic and Robust Engineering Design
19. Bidirectional Diffusion Bridge Models
    2025/02/12 by Duc Kieu, Kieu, Duc, Do, Kien +6 · 3 citations
    Mathematics · #Numerical methods for differential equations
20. Robust high-order low-rank BUG integrators based on explicit Runge--Kutta methods
    2025/02/10 by Fabio Nobile, Sébastien Riffaud, Nobile, Fabio +1 · 1 citation
    Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical methods for differential equations #cs.NA #math.DS #math.NA
21. A high order correction to the Lax-Friedrich's method for approximating stationary Hamilton-Jacobi equations
    2025/02/06 by Tom Lewis, Lewis, T., Xiaoping Xue +1 · 1 citation
    Mathematics · Computer Science · #Numerical methods for differential equations #Matrix Theory and Algorithms #Mathematical Biology Tumor Growth
22. A time adaptive multirate Quasi-Newton waveform iteration for coupled problems
    2025/02/05 by Niklas Kotarsky, Philipp Birken, Kotarsky, Niklas +1 · 1 citation
    Computer Science · Engineering · Mathematics · #65M22 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #G.1.8 #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Numerical methods for differential equations
23. Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms
    2025/02/01 by Yinuo Ren, Ren, Yinuo, Haoxuan Chen +14 · 1 voice · 17 citations
    Mathematics · Engineering · #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods
24. Parameter-Efficient Fine-Tuning for Foundation Models
    2025/01/23 by Dan Zhang, Tao Feng, Zhang, Dan +9 · 14 citations
    Mathematics · Engineering · #Numerical methods for differential equations #Civil and Structural Engineering Research
25. Disclinations, dislocations, and emanant flux at Dirac criticality
    2025/01/23 by Maissam Barkeshli, Barkeshli, Maissam, Christopher Fechisin +5 · 5 citations
    Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Numerical methods for differential equations #Quantum Chromodynamics and Particle Interactions #Strongly Correlated Electrons (cond-mat.str-el)
26. On the scalar sector of 2HDM: ring of basis invariants, syzygies, and six-loop renormalization-group equations
    2025/01/23 by A. V. Bednyakov, Bednyakov, A. V. · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations
27. Algebraicity and integrality of solutions to differential equations
    2025/01/22 by Yeuk Hay Joshua Lam, Daniel Litt, Lam, Yeuk Hay Joshua +1 · 1 voice · 1 citation
    Mathematics · #Numerical methods for differential equations
28. Freidlin-Wentzell type exit-time estimates for time-inhomogeneous diffusions and their applications
    2025/01/21 by Ashot Aleksian, Stéphane Villeneuve, Aleksian, Ashot +1 · 1 citation
    Computer Science · Mathematics · #60H10 #60J60 #60K35 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical methods for differential equations #Probability (math.PR)
29. Convergent Sixth-order Compact Finite Difference Method for Variable-Coefficient Elliptic PDEs in Curved Domains
    2025/01/17 by J.S. SIM, Han, Bin, Sim, Jiwoon · 3 citations
    Engineering · Mathematics · #35J25 #65N06 #65N12 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
30. Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
    2025/01/07 by Cinzia Elia, Roberta Fabbri, Elia, Cinzia +3 · 1 citation
    Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Numerical methods for differential equations #Quantum chaos and dynamical systems

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