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132 indexed repositories · View on GitHub

DifferentialEquations.jl
Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary ...

Julia · 3157 stars
SciMLBook
Parallel Computing and Scientific Machine Learning (SciML): Methods and Applications (MIT 18.337J/6.338J)

HTML · 2044 stars
ModelingToolkit.jl
An acausal modeling framework for automatically parallelized scientific machine learning (SciML) in Julia. A computer algebra system for ...

Julia · 1682 stars
NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated s...

Julia · 1228 stars
DiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs, and stiff+non-stiff DE solvers, demonstrating scientific machine learnin...

Julia · 926 stars
Optimization.jl
Mathematical Optimization in Julia. Local, global, gradient-based and derivative-free. Linear, Quadratic, Convex, Mixed-Integer, and Nonl...

Julia · 839 stars
OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE) and differential-algebraic equation (DAE) solvers, including neural ordinary differ...

Julia · 683 stars
diffeqpy
Solving differential equations in Python using DifferentialEquations.jl and the SciML Scientific Machine Learning organization

Python · 611 stars
Catalyst.jl
Chemical reaction network and systems biology interface for scientific machine learning (SciML). High performance, GPU-parallelized, and ...

Julia · 526 stars
BlackBoxOptim.jl
Black-box optimization for Julia

Julia · 464 stars
DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems for the SciML Scientific Machine Learning organization

Julia · 430 stars
SciMLSensitivity.jl
A component of the DiffEq ecosystem for enabling sensitivity analysis for scientific machine learning (SciML). Optimize-then-discretize, ...

Julia · 396 stars
Surrogates.jl
Surrogate modeling and optimization for scientific machine learning (SciML)

Julia · 382 stars
ComponentArrays.jl
Arrays with arbitrarily nested named components.

Julia · 375 stars
Evolutionary.jl
Evolutionary & genetic algorithms for Julia

Julia · 352 stars
SciMLBenchmarks.jl
Scientific machine learning (SciML) benchmarks, AI for science, and (differential) equation solvers. Covers Julia, Python (PyTorch, Jax),...

Julia · 346 stars
DiffEqDocs.jl
Documentation for the DiffEq differential equations and scientific machine learning (SciML) ecosystem

Julia · 328 stars
DiffEqGPU.jl
GPU-acceleration routines for DifferentialEquations.jl and the broader SciML scientific machine learning ecosystem

Julia · 327 stars
NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers (Newton methods), bracketed rootfinding (bisection, Falsi), with sparsity ...

Julia · 309 stars
LinearSolve.jl
LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, a...

Julia · 293 stars
112 more repositories live on View on GitHub

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CHOLMOD path never checks its LDLt fallback, so a sparse symmetric indefinite solve throws Open

Difficulty 4/5 3-5 days Newbie friendliness 72/100

SciML/LinearSolve.jl#1328 · Opened Sep 19, 2026
A shift applied to a whole array variable in a clock partition refers to an undeclared variable Open

Difficulty 4/5 3-5 days Newbie friendliness 52/100

SciML/ModelingToolkit.jl#5169 · Opened Sep 19, 2026
Linearizing a model that contains discrete callbacks (synchronous / clocked subsystems) Open

Difficulty 5/5 Over a week Newbie friendliness 28/100

SciML/ModelingToolkit.jl#5166 · Opened Sep 18, 2026
FirstOrder(lowpass=false): documented transfer function differs from implementation for k != 1 Open

bug

Difficulty 3/5 1-2 days Newbie friendliness 55/100

SciML/ModelingToolkitStandardLibrary.jl#515 · Opened Sep 17, 2026
InvPreconditioner aliases its input in the two-argument ldiv!, so preconditioned IterativeSolvers solves return the zero vector Open

Difficulty 3/5 1-2 days Newbie friendliness 82/100

SciML/LinearSolve.jl#1322 · Opened Sep 17, 2026
Metal and CUDA LU choices throw instead of falling back to QR, and report ReturnCode.Default when they succeed Open

Difficulty 3/5 1-2 days Newbie friendliness 74/100

SciML/LinearSolve.jl#1321 · Opened Sep 17, 2026
The CLAP host holds one plugin at a time, so a chain of two effects is not expressible Open

bot-generated enhancement needs-chris-review

Difficulty 5/5 Over a week Newbie friendliness 30/100

SciML/AudioPlugins.jl#58 · Opened Sep 17, 2026
Clarify differences between Presentation and Content MathML Open

Difficulty 2/5 1-2 days Newbie friendliness 74/100

SciML/MathML.jl#126 · Opened Sep 17, 2026
ForwardDiff extension: in-place updates to `cache.A` leave the primal matrix and partials stale, so `isfresh` solves the previous system Open

Difficulty 4/5 3-5 days Newbie friendliness 52/100

SciML/LinearSolve.jl#1315 · 1 comment · Opened Sep 14, 2026
Bounded LevenbergMarquardt with AutoEnzyme stalls at the initial point Open

Difficulty 4/5 3-5 days Newbie friendliness 55/100

SciML/NonlinearSolve.jl#1288 · Opened Sep 14, 2026
Most in-place factorizations ignore `alias_A`, destroying the caller's matrix on refactorization Open

Difficulty 4/5 3-5 days Newbie friendliness 68/100

SciML/LinearSolve.jl#1313 · 1 comment · Opened Sep 14, 2026
Reverse-mode `∂A` drops the residual term for non-square solves, disagreeing with forward mode Open

Difficulty 5/5 Over a week Newbie friendliness 38/100

SciML/LinearSolve.jl#1309 · Opened Sep 14, 2026
Extension LU algorithms never snapshot `A`, so the QR safety fallback restores a stale matrix Open

Difficulty 4/5 3-5 days Newbie friendliness 65/100

SciML/LinearSolve.jl#1306 · Opened Sep 14, 2026
Broyden/Klement on a Dual-valued NonlinearProblem: partials grow unboundedly while only value residuals are checked for convergence Open

Difficulty 5/5 Over a week Newbie friendliness 38/100

SciML/NonlinearSolve.jl#1283 · Opened Sep 14, 2026
Array-valued arguments of dependent variables and vector calculus (u(t, x) with x[1:d]) Open

Difficulty 4/5 3-5 days Newbie friendliness 48/100

SciML/NeuralPDE.jl#1181 · Opened Sep 13, 2026
Optimization-system driver: map replaced_vars back in the solution interface Open

Difficulty 3/5 1-2 days Newbie friendliness 68/100

SciML/PDEBase.jl#122 · Opened Sep 13, 2026
Lower array-valued constraints of a System into cons/lcons/ucons Open

Difficulty 4/5 3-5 days Newbie friendliness 58/100

SciML/ModelingToolkit.jl#5151 · Opened Sep 13, 2026
Re-enlarge the DGM tests and tutorial now that problem generation no longer scales with parameter count Open

Difficulty 2/5 1-3 hours Newbie friendliness 78/100

SciML/NeuralPDE.jl#1180 · Opened Sep 13, 2026
Emit MultiObjectiveOptimizationFunction for Systems with several costs Open

Difficulty 4/5 3-5 days Newbie friendliness 45/100

SciML/ModelingToolkit.jl#5150 · Opened Sep 13, 2026
NNSDE2 GBM weak-solve tolerance is sensitive to floating-point summation order Open

Difficulty 3/5 1-2 days Newbie friendliness 74/100

SciML/NeuralPDE.jl#1179 · Opened Sep 13, 2026
Sampling lifecycle: resample! caveats, seeded variant, and RNG consumption by symbolic_discretize Open

Difficulty 4/5 3-5 days Newbie friendliness 48/100

SciML/NeuralPDE.jl#1178 · Opened Sep 13, 2026
Transfer learning by distillation (neural_adapter of NeuralPDE 6) Open

Difficulty 5/5 Over a week Newbie friendliness 45/100

SciML/NeuralPDE.jl#1176 · Opened Sep 13, 2026
Adaptive loss weights as callbacks over the weights parameters Open

Difficulty 5/5 Over a week Newbie friendliness 48/100

SciML/NeuralPDE.jl#1177 · Opened Sep 13, 2026
Bayesian PINNs for PDEs on the rewritten pipeline Open

Difficulty 5/5 Over a week Newbie friendliness 35/100

SciML/NeuralPDE.jl#1175 · Opened Sep 13, 2026
General arguments of dependent variables: u(t, x + 1), u(2x) Open

Difficulty 4/5 3-5 days Newbie friendliness 55/100

SciML/NeuralPDE.jl#1174 · Opened Sep 13, 2026
GPU training for the rewritten PDE pipeline Open

Difficulty 4/5 3-5 days Newbie friendliness 55/100

SciML/NeuralPDE.jl#1172 · Opened Sep 13, 2026
Boundary conditions as exact constraints through a constrained solver Open

Difficulty 4/5 3-5 days Newbie friendliness 48/100

SciML/NeuralPDE.jl#1173 · Opened Sep 13, 2026
Forward-mode Enzyme derivative backend (AbstractDerivativeLowering) Open

Difficulty 5/5 Over a week Newbie friendliness 25/100

SciML/NeuralPDE.jl#1171 · Opened Sep 13, 2026
Make Enzyme the CPU default for the generated PINN objective Open

Difficulty 5/5 Over a week Newbie friendliness 35/100

SciML/NeuralPDE.jl#1170 · Opened Sep 13, 2026
Integro-differential equations in the rewritten parser Open

Difficulty 5/5 Over a week Newbie friendliness 35/100

SciML/NeuralPDE.jl#1169 · Opened Sep 13, 2026
write_possibly_indexed_array! should broadcast scalar values to array-shaped keys (remove write_dd_guess!) Open

Difficulty 3/5 1-2 days Newbie friendliness 72/100

SciML/ModelingToolkit.jl#5147 · Opened Sep 13, 2026
DAEProblem path: remake(prob; p) does not carry a parameter into the initial condition Open

Difficulty 4/5 3-5 days Newbie friendliness 55/100

SciML/MethodOfLines.jl#697 · Opened Sep 13, 2026
Complex equations are split wrongly: im * Dt(ψ) ~ Dxx(ψ) discretizes to -Dxx(Re ψ) ~ 0 and Dt(Im ψ) ~ 0 Open

Difficulty 4/5 3-5 days Newbie friendliness 58/100

SciML/MethodOfLines.jl#696 · Opened Sep 13, 2026
Continuous adjoints add d(sum(u0))/dp when u0 depends on parameters through initialization Open

Difficulty 4/5 3-5 days Newbie friendliness 58/100

SciML/SciMLSensitivity.jl#1663 · Opened Sep 13, 2026
Move the bounded finite-difference Jacobian stencil upstream to FiniteDiff.jl / DI Open

Difficulty 5/5 Over a week Newbie friendliness 38/100

SciML/NonlinearSolve.jl#1274 · Opened Sep 13, 2026
Continuous-callback adjoints fail converting FakeIntegrator state from SizedVector to MVector Open

Difficulty 3/5 1-2 days Newbie friendliness 74/100

SciML/SciMLSensitivity.jl#1660 · Opened Sep 13, 2026
OptimizationNOMAD does not compile Open

bug

Difficulty 3/5 1-2 days Newbie friendliness 64/100

SciML/Optimization.jl#1358 · 2 comments · Opened Sep 13, 2026
Bounded defaults fail for mixed scalar and array state/residual shapes Open

Difficulty 4/5 3-5 days Newbie friendliness 52/100

SciML/NonlinearSolve.jl#1270 · Opened Sep 13, 2026
Enzyme SCC initialization regresses at concretize_initializeprob on Julia 1.13 Open

Difficulty 5/5 Over a week Newbie friendliness 35/100

SciML/ModelingToolkit.jl#5140 · Opened Sep 13, 2026
Compile and generate code for whole-array equation models without scalarizing per element (tracking) Open

bot-generated needs-chris-review

Difficulty 5/5 Over a week Newbie friendliness 25/100

SciML/ModelingToolkit.jl#5139 · 1 comment · Opened Sep 13, 2026
Extension test environment setup writes read-only installed Project.toml on Julia 1.13 Open

Difficulty 3/5 1-2 days Newbie friendliness 76/100

SciML/Catalyst.jl#1561 · Opened Sep 13, 2026
Array parameter defaults and bindings given as slices of another array parameter fail in MTKParameters Open

bot-generated needs-chris-review

Difficulty 4/5 3-5 days Newbie friendliness 35/100

SciML/ModelingToolkit.jl#5138 · Opened Sep 13, 2026
Keep discretized dependent variables as array-valued unknowns instead of scalarizing per grid point Open

Difficulty 5/5 Over a week Newbie friendliness 35/100

SciML/MethodOfLines.jl#695 · 1 comment · Opened Sep 13, 2026
Master CUDA CI: GPUVern7 callback test compares opposite sides of the final bounce Open

Difficulty 4/5 3-5 days Newbie friendliness 35/100

SciML/DiffEqGPU.jl#540 · Opened Sep 13, 2026
Remaining CI failures on master: JET typo-mode findings and MPI parallel output tests Open

Difficulty 4/5 3-5 days Newbie friendliness 38/100

SciML/Dedalus.jl#15 · Opened Sep 12, 2026
Flaky: downgrade Initialization `use_scc = true` gradient test returns 1e153 (Dual solve goes non-finite at t=0) Open

Difficulty 4/5 3-5 days Newbie friendliness 35/100

SciML/ModelingToolkit.jl#5125 · 1 comment · Opened Sep 12, 2026
Parser rewrite follow-ups: integrals, Enzyme/GPU, exact constraints, array coordinates, Bayesian PDEs Open

Difficulty 5/5 Over a week Newbie friendliness 20/100

SciML/NeuralPDE.jl#1166 · Opened Sep 12, 2026
Preserve array flow balances when expanding ordinary connector connections Open

bot-generated needs-chris-review

Difficulty 4/5 3-5 days Newbie friendliness 30/100

SciML/ModelingToolkit.jl#5119 · Opened Sep 12, 2026
Unit validation crashes on causal variable `connect`: `unknowns(::BasicSymbolic)` MethodError in MTKDynamicQuantitiesExt Open

Difficulty 2/5 1-3 hours Newbie friendliness 78/100

SciML/ModelingToolkit.jl#5118 · Opened Sep 12, 2026
Coverage sweep: operations tracing emits that the rule table does not recognize (25 gaps, 3 unsound) Open

Difficulty 5/5 Over a week Newbie friendliness 42/100

SciML/SymbolicAnalysis.jl#156 · 3 comments · Opened Sep 12, 2026

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