Julia: A Fresh Approach to Numerical Computing

2017/01/01 by Jeff Bezanson, Alan Edelman, Stefan Karpinski +1 · 6,366 citations
Computer Science · #Abstraction #Bridging (networking) #Code (set theory) #Computation #Computer science #Distributed and Parallel Computing Systems #Parallel Computing and Optimization Techniques #Programmer #Programming language #Quantum Computing Algorithms and Architecture #Set (abstract data type) #Theoretical computer science

paper · doi:10.1137/141000671

published in SIAM Review 59(1), 65-98 (Society for Industrial and Applied Mathematics)

openalex publication_date 2017/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast and questions notions generally held to be “laws of nature" by practitioners of numerical computing: \beginlist \item High-level dynamic programs have to be slow. \item One must prototype in one language and then rewrite in another language for speed or deployment. \item There are parts of a system appropriate for the programmer, and other parts that are best left untouched as they have been built by the experts. \endlist We introduce the Julia programming language and its design---a dance between specialization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, which is what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can achieve machine performance without sacrificing human convenience.

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• Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics
• Nonstationary Distribution Estimation via Wasserstein Probability Flows
• MultiObjectiveAlgorithms.jl: a Julia package for solving multi-objective optimization problems
• Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates
• The Exact Asymptotic Form of Bayesian Generalization Error in Latent Dirichlet Allocation
• Physical Informed Neural Networks for modeling ocean pollutant
• A note on Global Positioning System (GPS) and Euclidean distance matrices
• Imaginary multiquadratic number fields of exponent 3 and 5
• On the non-convexity issue in the radial Calderón problem
• MathOptAI.jl: Embed trained machine learning predictors into JuMP models
• Quasiconservation Laws and Suppressed Transport in Weakly Interacting Localized Models
• HPR-QP: A dual Halpern Peaceman-Rachford method for solving large-scale convex composite quadratic programming
• Turbulence in Simulated Local Cluster Analogs: one-to-one comparisons between SLOW and XRISM/Hitomi
• An Algorithm for Automated Extraction of Resonance Parameters from the Stabilization Method
• eGHWT: The Extended Generalized Haar-Walsh Transform
• On the Orbit of the Binary Brown Dwarf Companion GL229 Ba and Bb
• MIMIX: A Bayesian Mixed-Effects Model for Microbiome Data From Designed Experiments
• Discovery of the Hidden State in Ionic Models Using a Domain-Specific Recurrent Neural Network
• Thermodynamic ranking of pathways in reaction networks
• Elimination of angular dependency in the quantum three-body problem made easy
• On the Out-of-Sample Performance of Stochastic Dynamic Programming and Model Predictive Control
• FractionalDiffEq.jl: High Performance Fractional Differential Equation Solver in Julia
• Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
• Reinforcement Learning for Optimal Control of Spin Magnetometers
• Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis
• DistStat.jl: Towards Unified Programming for High-Performance Statistical Computing Environments in Julia
• Multiscale Stochastic Simulation of the US Pacific Northwest Using Distributed Computing and Databases with Integrated Inflow and Variable Renewable Energy
• Approximating the order 2 quantum Wasserstein distance using the moment-SOS hierarchy
• Geometric Computing with Chain Complexes: Design and Features of a Julia Package
• The QuiverTools package for SageMath and Julia
• Circuitscape in Julia: High Performance Connectivity Modelling to Support Conservation Decisions
• A Scenario-based Model Predictive Control Scheme for Pandemic Response through Non-pharmaceutical Interventions
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• On circumcentered direct methods for monotone variational inequality problems
• Quantum Circuits in Additive Hilbert Space
• AP-Perf: Incorporating Generic Performance Metrics in Differentiable Learning
• Random time-shift approximation enables hierarchical Bayesian inference of mechanistic within-host viral dynamics models on large datasets
• Tree-based adaptive finite element methods for deformable image registration
• On the Effectiveness of Classical Regression Methods for Optimal Switching Problems
• FTheoryTools: Advancing Computational Capabilities for F-Theory Research
• An exact algorithm for the static pricing problem under discrete mixed logit demand
• Pressure torque of torsional Alfvén modes acting on an ellipsoidal mantle
• A Minimum Distance Estimator Approach for Misspecified Ergodic Processes
• Accurate Reduced Floating-Point Precision Implicit Monte Carlo
• Automatic differentiation for Lax-Wendroff-type discretizations
• Nonlinear classifiers for ranking problems based on kernelized SVM
• Fast parallel transient electromagnetic modeling using a uniform-in-time approximation to the exponential
• Operator Fitting for Parameter Estimation of Stochastic Differential Equations
• Coronary artery calcium quantification technique using dual energy material decomposition: a simulation study
• On the relation of powerflow and Telegrapher's equations: continuous and numerical Lyapunov stability
• Prediction and control of geometry-induced nematic order in growing multicellular systems
• An empirical Bayes approach to identification of modules in dynamic networks
• On Inexact Accelerated Proximal Gradient Methods with Relative Error Rules
• The SagbiHomotopy.jl package for solving polynomial systems
• Wasserstein Distributionally Robust Inverse Multiobjective Optimization
• Monitoring data in R with the lumberjack package
• A Framework for Democratizing AI
• Breakdown of the optical saturation regime in molecular single-photon emitters
• Random projection of Linear and Semidefinite problem with linear inequalities
• Minimizers of one-dimensional regularization problems with linear and nonlinear total variation
• Contraction L₁-Adaptive Control using Gaussian Processes
• Low-memory stochastic backpropagation with multi-channel randomized\n trace estimation
• Convexification of box-constrained polynomial optimization problems via monomial patterns
• HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
• Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems
• A Class Inference Scheme With Dempster-Shafer Theory for Learning Fuzzy-Classifier Systems
• Graph-Based Modeling and Simulation of Complex Systems
• Defect states in compressible active polar fluids with turnover
• Stokes Waves in Water of Finite Depth
• Tensor Renormalization Group Meets Computer Assistance
• Second-Order-Cone Formulations of Power Flow for Topology Optimization
• Accelerating delayed-acceptance Markov chain Monte Carlo algorithms
• Online Competitive Information Gathering for Partially Observable Trajectory Games
• An Overview of GPU-based First-Order Methods for Linear Programming and Extensions
• Discrete Adjoints for Accurate Numerical Optimization with Application to Quantum Control
• Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation
• Optimal Survival Trees
• Parametric level-set inverse problems with stochastic background estimation
• Efficient sampling for sparse Bayesian learning using hierarchical prior normalization
• Learning Parametric Distributions from Samples and Preferences
• Information Theoretic Regret Bounds for Online Nonlinear Control
• Bridging Unstratified and Stratified Simulations of the Streaming Instability for τ_s=0.1 Grains
• A Julia toolkit for species distribution data
• Neuromorphic computing with a single qudit
• PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flow
• Levitating frogs, machine learning and elliptic integrals
• DualSchool: How Reliable are LLMs for Optimization Education?
• Pair correlation for Dedekind zeta functions of abelian extensions
• Accelerated Computation and Tracking of AC Optimal Power Flow Solutions using GPUs
• AutoSGD: Automatic Learning Rate Selection for Stochastic Gradient Descent
• Developing hybrid mechanistic and data-driven personalized prediction models for platelet dynamics
• Accurate solar-power integration: Solar-weighted Gaussian quadrature
• Quantum computation of hadron scattering in a lattice gauge theory
• Scattering of compact kinks
• A General Framework for Survival Analysis and Multi-State Modelling
• Learning Structure in Nested Logit Models
• Perceptual decision making: Biases in post-error reaction times explained by attractor network dynamics
• Pick-and-Mix Information Operators for Probabilistic ODE Solvers
• Exploiting term sparsity in Noncommutative Polynomial Optimization
• Anti-brane singularities as red herrings
• Parallelizing the Circumcentered-Reflection Method
• An ideal-sparse generalized moment problem reformulation for completely positive tensor decomposition exploiting maximal cliques of multi-hypergraphs
• New Understandings and Computation on Augmented Lagrangian Methods for Low-Rank Semidefinite Programming
• Numerical Irreducible Decomposition in Julia
• Comparing Parameterizations and Objective Functions for Maximizing the Volume of Zonotopic Invariant Sets
• Orthogonal Trace-Sum Maximization: Applications, Local Algorithms, and Global Optimality
• X-KAN: Optimizing Local Kolmogorov-Arnold Networks via Evolutionary Rule-Based Machine Learning
• Extreme mass distributions for quasi-copulas
• Inverse Multiobjective Optimization Through Online Learning
• cuHALLaR: A GPU Accelerated Low-Rank Augmented Lagrangian Method for Large-Scale Semidefinite Programming
• FESOM2-JAX v1.0: a differentiable shadow of the ocean-sea-ice model FESOM2, cast onto GPUs
• BROUTE: a benchmark suite for the implementation of standard vehicle routing algorithms
• Evolutionary–developmental (evo-devo) dynamics of hominin brain size
• Bifurcation of elastic curves with modulated stiffness
• GPU-Accelerated SPOCK for Scenario-Based Risk-Averse Optimal Control Problems
• Prosody leaks into the memories of words
• Encoding prior knowledge in ensemble refinement
• Interlimb coordination in Parkinson’s Disease is minimally affected by a visuospatial dual task
• Mixed-model Log-likelihood Evaluation Via a Blocked Cholesky Factorization
• Competition and Investment Model of Wealth Distribution
• Sobolev Training of End-to-End Optimization Proxies
• Exploring Variational Entanglement Hamiltonians
• High-Order Hermite Optimization: Fast and Exact Gradient Computation in Open-Loop Quantum Optimal Control using a Discrete Adjoint Approach
• Accelerating the time-domain LISA response model with central finite differences and hybridization techniques
• Convex Optimization for Trajectory Generation
• A Look at Communication-Intensive Performance in Julia
• Differentiable Physics: A Position Piece
• A column-generation-based matheuristic for periodic train timetabling with integrated passenger routing
• An aggregating strategy for shifting experts in discrete sequence prediction
• Two-Level Sketching Alternating Anderson acceleration for Complex Physics Applications
• Optimal adaptive two-stage designs for single-arm trial with binary endpoint
• Updating the SiD Detector concept
• Interdependent Phenotypic and Biogeographic Evolution Driven by Biotic Interactions
• Smooth optimization using global and local low-rank regularizers
• Structure determination from single-molecule X-ray scattering images using stochastic gradient ascent
• Simple generators of rational function fields
• Hot-Starting the Ac Power Flow with Convolutional Neural Networks
• Uncertainty in marine weather routing
• BSTModelKit.jl: A Julia Package for Constructing, Solving, and Analyzing Biochemical Systems Theory Models
• Compressive sensing and truncated moment problems on spheres
• Curating Metal–Organic Frameworks To Compose Robust Gas Sensor Arrays in Dilute Conditions
• 3264 Conics in a Second
• DiFVM: A Vectorized Graph-Based Finite Volume Solver for Differentiable CFD on Unstructured Meshes
• NEP-PACK: A Julia package for nonlinear eigenproblems - v0.2
• Storage and selection of multiple chaotic attractors in minimal reservoir computers
• Interactions between nascent proteins translated by adjacent ribosomes drive homomer assembly
• Efficient Krylov methods for linear response in plane-wave electronic structure calculations
• Scorio.jl: A Julia package for ranking stochastic responses
• Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
• Low Precision Fortran -- Enabling Low Precision Floating Point Arithmetic in Modern Fortran
• Mojo: A Promising Tool for Scalable Financial AI Efficiency
• A randomized Halton algorithm in R
• From debt crises to financial crashes (and back): a stock-flow consistent model for stock price bubbles
• A natural language framework for non-conforming hybrid polytopal methods in Gridap.jl
• Aldebaran b's temperate past uncovered in planet search data
• Assessing and Visualizing Matrix Variate Normality
• An Imaging Search for Post-Main-Sequence Planets of Sirius B
• QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
• Computing points in connected components defined by a real inequation: algorithms, complexity and implementations, Part I
• 3D mechano-geometric multicellular model of apical stem cell-driven plant morphogenesis
• Personality traits of special forces operators: Comparing commandos, candidates, and controls.
• Interprocess Communication of Algebraic Data
• Approximating neutron-star radii using gravitational-wave only measurements with symbolic regression
• RotorMap and Quantum Fingerprints of DNA Sequences via Rotary Position Embeddings
• Decoherence of Morse Oscillator in the Presence of Dissipationless Environment
• Constructing Magic Squares: an integer constraint satisfaction problem and a fast approach
• LCS.jl: A High-Performance, Multi-Platform Computational Model in Julia for Turbulent Particle-Laden Flows
• Branch-and-Bound Tensor Networks for Exact Ground-State Characterization
• The Deep Learning Compiler: A Comprehensive Survey
• Formulations and Approximations of the Branch Flow Model for Mesh Power Networks
• Algebraic Statistics in OSCAR
• How to Improve Portuguese Secondary Education
• Hierarchical Recursive Precision for Accelerating Symmetric Linear Solves on MXUs
• Tensor Algebra Processing Primitives (TAPP): Towards a Standard for Tensor Operations
• FormulaCompiler.jl and Margins.jl: Efficient Marginal Effects in Julia
• Origin of Frequency Clusters and Self-Organized Triplet Locking in the Kuramoto Model with Inertia
• Knapsack with compactness: a semidefinite approach
• Investigation of Optical functions, sub-bandgap transitions, and Urbach tail in the absorption spectra of Ga2O3 thin films deposited using mist-CVD
• A guide to modeling plasmid co-infection dynamics
• Pulsed Magnetophononics in Gapped Quantum Magnets
• \text Aut(\mathbb F₅) has property (T)
• Learning of Colors from Color Names: Distribution and Point Estimation
• GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems
• A New Deterministic Technique for Symbolic Regression
• Nonparametric Bayesian Volatility Estimation
• Binarity at LOw Metallicity (BLOeM): Bayesian inference of natal kicks from inert black hole binaries
• Inducing spectral gaps for the cohomological Laplacians of Sp_2n(ℤ)
• Vector Operations for Accelerating Expensive Bayesian Computations – A Tutorial Guide
• Schelling segregation dynamics in densely-connected social network graphs
• An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method
• Autonomous materials synthesis via hierarchical active learning of nonequilibrium phase diagrams
• Moment Ideals of Local Dirac Mixtures
• Artificial Benchmark for Community Detection (ABCD)—Fast random graph model with community structure
• Detector of microwave photon pairs based on a Josephson photomultiplier
• Simple and Scalable Sparse k-means Clustering via Feature Ranking
• Hydrogen adatoms on graphene: The role of hybridization and lattice distortion
• Reinforcement Learning and Metaheuristics for Feynman Integral Reduction
• Computation of Tight Enclosures for Laplacian Eigenvalues
• Optimal stochastic unraveling of disordered open quantum systems: Application to driven-dissipative photonic lattices
• Topology optimization of nonlinear elastic micro-structures by a domain reduction technique
• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Modeling and Computation of Kubo Conductivity for 2D Incommensurate Bilayers
• High‐resolution in vivo MR‐STAT using a matrix‐free and parallelized reconstruction algorithm
• Automatic Generation of Interpolants for Lattice Samplings: Part II -- Implementation and Code Generation
• Recursive Optimization of Finite Blocklength Allocation to Mitigate Age-of-Information Outage
• Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
• Bayesian Model Averaging in Causal Instrumental Variable Models
• AIDA: An Active Inference-based Design Agent for Audio Processing Algorithms
• Array languages make neural networks fast
• Phonon Casimir effect in polyatomic systems
• Modelling and optimisation of water management in sloping coastal aquifers with seepage, extraction and recharge
• Density matrices approximation for electronic structure calculations
• Piecewise Semi-Ellipsoidal Control Invariant Sets
• Flat topological bands and eigenstate criticality in a quasiperiodic insulator
• Node-Based Job Scheduling for Large Scale Simulations of Short Running Jobs
• Covariate-Powered Empirical Bayes Estimation
• Characterizing steady states of genome-scale metabolic networks in continuous cell cultures
• Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
• Decompounding discrete distributions: A nonparametric Bayesian approach
• Estimating leverage scores via rank revealing methods and randomization
• Short-time approximate solutions of an equation modeling a camphor motion
• Approximating Optimal Points of a Lebesgue Constant Proxy for Interpolation in the Simplex
• Optimal Convergence Rates for Generalized Alternating Projections
• Learning to Recombine and Resample Data for Compositional Generalization
• Numerical evaluation of time-distance helioseismic sensitivity kernels in spherical geometry
• Phase transition into an instanton crystal state
• Quantum reservoir computing with a single nonlinear oscillator
• Faster multivariate integration in D-modules
• Extrae.jl: Julia bindings for the Extrae HPC Profiler
• Axisymmetric squirmers in Stokes fluid with nonuniform viscosity
• Bartlett Couplings of the Onion and Vine LKJ Samplers
• An inverse mixed-integer optimization framework for learning interpretable models of expert decision making
• ChromOps.jl: High-order simulation and discrete forward sensitivity analysis for chromatography models
• nonprobsvy -- An R package for modern methods for non-probability surveys
• Diagnostic Uncertainty Limits the Potential of Early Warning Signals to Identify Epidemic Emergence
• Inverse design of multiresonance filters via quasi-normal mode theory
• Sectoral and spatial decomposition methods for multi-sector capacity expansion models
• Navigator readouts with optimized processing improve spinal cord and gray matter segmentability in multi-echo gradient-echo imaging
• Time-local stochastic equation of motion for solid ionic electrolytes
• Relaxed Weak Accelerated Proximal Gradient Method: a Unified Framework for Nesterov's Accelerations
• Bayesian Component Separation for DESI LAE Automated Spectroscopic Redshifts and Photometric Targeting
• Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions
• Learning algebraic varieties from samples
• Assessing the Role of Intrinsic Variability in Black Hole Parameter Inference using Multi-Epoch EHT Data
• Julia (programming language) [wikipedia]
• Multiple dispatch [wikipedia]
• Numerical analysis [wikipedia]
• MentaLiST - A fast MLST caller for large MLST schemes. [europepmc]
• Bone remodeling: A tissue-level process emerging from cell-level molecular algorithms. [europepmc]
• Integrated structural variation and point mutation signatures in cancer genomes using correlated topic models. [europepmc]
• Accuracy of parameter estimation for auto-regulatory transcriptional feedback loops from noisy data. [europepmc]
• Visbrain: A Multi-Purpose GPU-Accelerated Open-Source Suite for Multimodal Brain Data Visualization. [europepmc]
• Introduction of Tau Oligomers into Cortical Neurons Alters Action Potential Dynamics and Disrupts Synaptic Transmission and Plasticity. [europepmc]
• CTCF confers local nucleosome resiliency after DNA replication and during mitosis. [europepmc]
• Ordered multinomial regression for genetic association analysis of ordinal phenotypes at Biobank scale. [europepmc]
• Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data. [europepmc]
• Measuring the distribution of fitness effects in somatic evolution by combining clonal dynamics with dN/dS ratios. [europepmc]
• Array programming with NumPy. [europepmc]
• Power-law distribution in the number of confirmed COVID-19 cases. [europepmc]
• Identifiability analysis for stochastic differential equation models in systems biology. [europepmc]
• The impact of ventilation-perfusion inequality in COVID-19: a computational model. [europepmc]
• A Registration and Deep Learning Approach to Automated Landmark Detection for Geometric Morphometrics. [europepmc]
• Fixation patterns in simple choice reflect optimal information sampling. [europepmc]
• Time-Lagged Independent Component Analysis of Random Walks and Protein Dynamics. [europepmc]
• EntropyHub: An open-source toolkit for entropic time series analysis. [europepmc]
• MUON: multimodal omics analysis framework. [europepmc]
• Implementation of residue-level coarse-grained models in GENESIS for large-scale molecular dynamics simulations. [europepmc]
• The ribosome stabilizes partially folded intermediates of a nascent multi-domain protein. [europepmc]
• Bayesian parameter estimation for dynamical models in systems biology. [europepmc]
• The molecular cytoarchitecture of the adult mouse brain. [europepmc]
• Unlocking bacterial potential to reduce farmland N 2 O emissions. [europepmc]
• Molecular mimicry as a mechanism of viral immune evasion and autoimmunity. [europepmc]

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