Neural Differential Equations ML Frameworks

Frameworks and implementations for Neural ODEs, Neural CDEs, Neural SDEs, and related neural operators that learn dynamics through differential equations. Includes solvers, applications to time series and PDEs, but does NOT include general deep learning frameworks, standard RNNs, or non-neural PDE solvers.

There are 111 neural differential equations frameworks tracked. 1 score above 70 (verified tier). The highest-rated is lululxvi/deepxde at 71/100 with 3,954 stars. 1 of the top 10 are actively maintained.

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#	Framework	Score	Tier	Stars	Language
1	lululxvi/deepxde A library for scientific machine learning and physics-informed learning	71	Verified	3,954	Python
2	pnnl/neuromancer Pytorch-based framework for solving parametric constrained optimization...	67	Established	1,295	Python
3	wilsonrljr/sysidentpy A Python Package For System Identification Using NARMAX Models	65	Established	484	Python
4	dynamicslab/pysindy A package for the sparse identification of nonlinear dynamical systems from data	64	Established	1,774	Python
5	google-research/torchsde Differentiable SDE solvers with GPU support and efficient sensitivity analysis.	62	Established	1,708	Python
6	analysiscenter/pydens PyDEns is a framework for solving Ordinary and Partial Differential...	58	Established	314	Jupyter Notebook
7	NeuroDiffGym/neurodiffeq A library for solving differential equations using neural networks based on...	58	Established	773	Python
8	arsedler9/lfads-torch A PyTorch implementation of Latent Factor Analysis via Dynamical Systems...	57	Established	127	Jupyter Notebook
9	patrick-kidger/torchcde Differentiable controlled differential equation solvers for PyTorch with GPU...	55	Established	475	Python
10	NBoulle/greenlearning Learning Green's functions of partial differential equations with deep learning.	53	Established	71	Python
11	Tim-Salzmann/l4casadi Use PyTorch Models with CasADi for data-driven optimization or...	53	Established	560	Python
12	yataobian/awesome-ebm Collecting research materials on energy/entropy based models	52	Established	368	Shell
13	jbramburger/DataDrivenDynSyst Scripts and notebooks to accompany the book Data-Driven Methods for Dynamic Systems	52	Established	161	Jupyter Notebook
14	thuml/Neural-Solver-Library A Library for Advanced Neural PDE Solvers.	51	Established	281	Python
15	greydanus/hamiltonian-nn Code for our paper "Hamiltonian Neural Networks"	51	Established	510	Jupyter Notebook
16	GaloisInc/dlkoopman A general-purpose Python package for Koopman theory using deep learning.	51	Established	120	Python
17	martenlienen/torchode A parallel ODE solver for PyTorch	50	Established	276	Python
18	scDiffEq/scdiffeq-analyses Companion to https://github.com/scDiffEq/scDiffEq	50	Established	4	Jupyter Notebook
19	raminmh/CfC Closed-form Continuous-time Neural Networks	49	Emerging	1,014	Python
20	pswpswpsw/nif A library for dimensionality reduction on spatial-temporal PDE	49	Emerging	73	Jupyter Notebook
21	aleximmer/Laplace Laplace approximations for Deep Learning.	49	Emerging	535	Python
22	Koopman-Laboratory/KoopmanLab A library for Koopman Neural Operator with Pytorch.	49	Emerging	321	Python
23	camlab-ethz/ConvolutionalNeuralOperator This repository is the official implementation of the paper Convolutional...	49	Emerging	210	Python
24	decargroup/pykoop Koopman operator identification library in Python, compatible with `scikit-learn`	48	Emerging	104	Python
25	vavrines/Kinetic.jl Universal modeling and simulation of fluid mechanics upon machine learning....	48	Emerging	144	Julia
26	SciML/HighDimPDE.jl A Julia package for Deep Backwards Stochastic Differential Equation (Deep...	48	Emerging	84	Julia
27	EthanJamesLew/AutoKoopman AutoKoopman - automated Koopman operator methods for data-driven dynamical...	47	Emerging	81	Python
28	Zymrael/awesome-neural-ode A collection of resources regarding the interplay between differential...	46	Emerging	1,519	—
29	DiffEqML/torchdyn A PyTorch library entirely dedicated to neural differential equations,...	45	Emerging	1,555	Jupyter Notebook
30	cooper-org/cooper A general-purpose, deep learning-first library for constrained optimization...	45	Emerging	153	Python
31	IBM/simulai A toolkit with data-driven pipelines for physics-informed machine learning.	45	Emerging	197	Python
32	ctu-vras/monoforce [IROS 2024] [ICML 2024 Workshop Differentiable Almost Everything] MonoForce:...	45	Emerging	89	Jupyter Notebook
33	xwinxu/bayeSDE Code for "Infinitely Deep Bayesian Neural Networks with Stochastic...	44	Emerging	174	Python
34	patrick-kidger/Deep-Signature-Transforms Code for "Deep Signature Transforms" (NeurIPS 2019)	44	Emerging	98	Jupyter Notebook
35	patrick-kidger/NeuralCDE Code for "Neural Controlled Differential Equations for Irregular Time...	44	Emerging	700	Python
36	patrick-kidger/signatory Differentiable computations of the signature and logsignature transforms, on...	43	Emerging	298	C++
37	qiauil/torchfsm TorchFSM: Fourier Spectral Method with PyTorch	43	Emerging	56	Python
38	fregu856/ebms_regression Official implementation of "Energy-Based Models for Deep Probabilistic...	43	Emerging	106	Jupyter Notebook
39	raj-gun/NonSysID A MatLab package for System Identification using linear and nonlinear...	43	Emerging	5	MATLAB
40	samholt/NeuralLaplace Neural Laplace: Differentiable Laplace Reconstructions for modelling any...	42	Emerging	82	Python
41	thuml/Koopa Code release for "Koopa: Learning Non-stationary Time Series Dynamics with...	42	Emerging	240	Python
42	yriyazi/Koopman-Operator-and-Deep-Neural-Networks-ISAV2023 In this work, we present a novel approach that combines the power of...	41	Emerging	10	Jupyter Notebook
43	ODINN-SciML/DiffEqSensitivity-Review A Review of Sensitivity Methods for Differential Equations	41	Emerging	34	TeX
44	AlexandraBaier/deepsysid System identification toolkit for multistep prediction using deep learning...	40	Emerging	18	Python
45	HaidaQuant/DeepBSDE Python code for solving partial differential equations (PDEs) using deep...	40	Emerging	27	Jupyter Notebook
46	filippo-masi/Thermodynamics-Neural-Networks Thermodynamics-based Artificial Neural Networks	40	Emerging	32	Jupyter Notebook
47	williamgilpin/fnn Embed strange attractors using a regularizer for autoencoders	39	Emerging	135	Jupyter Notebook
48	PEREGRINE-GW/peregrine A simulation-based Inference (SBI) library designed to perform analysis on a...	38	Emerging	17	Python
49	qiauil/ConvDO Convolutional Differential Operators for Physics-based Deep Learning Study	38	Emerging	26	Python
50	slimgroup/FNO4CO2 Learned coupled inversion for carbon sequestration monitoring and...	38	Emerging	23	Julia
51	phy-q/benchmark Phy-Q: A Testbed for Physical Reasoning	37	Emerging	45	Python
52	DiffEqML/diffeqml-research This repository contains code released by DiffEqML Research	37	Emerging	94	Jupyter Notebook
53	decargroup/closed_loop_koopman Companion code for Closed-Loop Koopman Operator Approximation	37	Emerging	16	Python
54	Hy23333/PFNN Official implementation of Learning Dissipative Chaos In A Linear Way	37	Emerging	15	Jupyter Notebook
55	Midhun-Kanadan/Machine-Learning-Models-for-Topology-Optimization This project explores the integration of Machine Learning (ML) and Deep...	37	Emerging	17	Jupyter Notebook
56	matlab-deep-learning/constrained-deep-learning Constrained deep learning is an advanced approach to training deep neural...	36	Emerging	70	MATLAB
57	ELIFE-ASU/INNLab A python/pytorch package for invertible neural networks	36	Emerging	71	Python
58	peterparity/conservation-laws-manifold-learning Discovering Conservation Laws using Optimal Transport and Manifold Learning	36	Emerging	22	Jupyter Notebook
59	Francis-Fan-create/SCaSML ScaSML solver for high dimensional gradient dependent semilinear PDE	36	Emerging	6	Python
60	halimarefat/torchFOAM Using PyTorch within OpenFOAM	35	Emerging	14	Jupyter Notebook
61	Zheng-Meng/Dynamics-Reconstruction-ML Published in Nature Communications: Bridging known and unknown dynamics by...	35	Emerging	9	Python
62	Ranlot/single-parameter-fit Real numbers, data science and chaos: How to fit any dataset with a single parameter	35	Emerging	650	Jupyter Notebook
63	HoangP8/torchidl torchidl: a general library for implicit models	35	Emerging	9	Python
64	Laborieux-Axel/holomorphic_eqprop Repository to reproduce the results of the paper "Holomorphic Equilibrium...	33	Emerging	11	Jupyter Notebook
65	bizoffermark/neural_wos Neural Walk-on-Spheres	33	Emerging	23	Python
66	jambo6/neuralRDEs Code for: "Neural Rough Differential Equations for Long Time Series", (ICML 2021)	32	Emerging	123	Jupyter Notebook
67	mbchang/dynamics A Compositional Object-Based Approach to Learning Physical Dynamics	32	Emerging	174	Lua
68	Axect/Neural_Hamilton Official implementation of the paper "Neural Hamilton: Can A.I. Understand...	31	Emerging	14	Python
69	tomoleary/dino Derivative-Informed Neural Operator: An Efficient Framework for...	31	Emerging	18	Python
70	psellcam/LaplaceNet A PyTorch Implementation of LaplaceNet:A Hybrid Energy-Neural Model for Deep...	30	Emerging	15	Shell
71	da03/Residual-EBM Code for Residual Energy-Based Models for Text Generation in PyTorch.	30	Emerging	26	Jupyter Notebook
72	decargroup/robust_observer_koopman Companion code for Uncertainty Modelling and Robust Observer Synthesis using...	29	Experimental	9	Python
73	Zheng-Meng/Parameter-Tracking-with-Machine-Learning Codes for ''Machine-learning parameter tracking with partial state...	29	Experimental	7	MATLAB
74	msakarvadia/operator_aliasing Studying if/how alising happens when PDE solutions are learned at different...	29	Experimental	6	Python
75	JakobEliasWagner/NeuralOperators Neural Operators with Applications to the Helmholtz Equation	28	Experimental	11	Python
76	ameya98/ActionAngleNetworks The official JAX implementation of Action-Angle Networks!	28	Experimental	10	Jupyter Notebook
77	jambo6/online-neural-cdes Code for: "Neural Controlled Differential Equations for Online Prediction Tasks"	28	Experimental	41	Python
78	filippo-masi/NICE Neural integration for constitutive equations	27	Experimental	13	Jupyter Notebook
79	dimitra-maoutsa/odes_for_sdes Deterministic particle dynamics for simulating Fokker-Planck probability flows	27	Experimental	26	Jupyter Notebook
80	pz33y/SynechismCore Stabilized Neural ODEs outperform Transformers on spatiotemporal chaos...	27	Experimental	1	Python
81	tsuboshun/LearnEntropy This repository estimates the entropy production rate from trajectory data...	27	Experimental	8	HTML
82	YichengDWu/NeuralGraphPDE.jl Integrating Neural Ordinary Differential Equations, the Method of Lines, and...	27	Experimental	18	Julia
83	haozhg/odmd-matlab Matlab implementation of online and window dynamic mode decomposition algorithms	27	Experimental	12	MATLAB
84	liuyao12/ConvNets-PDE-perspective an Open Collaborative project to explore the implications — theoretical or...	26	Experimental	21	Jupyter Notebook
85	kaist-silab/awesome-graph-pde Collection of resources about partial differential equations, graph neural...	26	Experimental	96	—
86	TOAQ-oss/nonlinear-affective-dynamics Official implementation of the paper "Non-Linear Computational Modeling of...	25	Experimental	2	Python
87	Alexin-CH/ReflectorML Hybrid ML/PIML freeform reflector design	25	Experimental	7	Python
88	NiuTrans/ODEs-in-Vision-and-Language An introduction to ODEs and their applications in vision and language	24	Experimental	13	HTML
89	Emory-Melody/awesome-epidemic-modeling-papers [KDD 2024] Papers about deep learning in epidemic modeling.	24	Experimental	66	—
90	NekkittAY/DMD-Neural-Operator DMD Neural Operator - A neural operator using DMD analysis to approximate the PDEs	24	Experimental	3	Jupyter Notebook
91	anac0der/fno_from_scratch Implementation of Fourier Neural Operator from scratch	23	Experimental	4	Jupyter Notebook
92	pcpet/intervalNets Interval arithmetic toolkit for PyTorch with certified interval forward...	22	Experimental	—	Jupyter Notebook
93	1ksev/Dynamic-Systems-Analysis 🏎️ Model and simulate vehicle suspension dynamics using Python and Laplace...	21	Experimental	—	TeX
94	timkimd/plnde Code for "Inferring Latent Dynamics Underlying Neural Population Activity...	21	Experimental	14	Julia
95	eth-siplab/Frequency-weighted-neural-Kalman-filters FW-NKF: Frequency-Weighted Neural Kalman Filters -- Official implementation....	21	Experimental	—	Python
96	erik2810/differentiable-physics-engine Browser-based differentiable physics demo: neural network learns and...	21	Experimental	—	JavaScript
97	dandip/ssinn Code for the paper "Sparse Symplectically Integrated Neural Networks"	21	Experimental	7	Python
98	lmotte/controlled-sde-learn Python implementation of the SDE estimation method proposed in...	20	Experimental	6	Python
99	pvlachas/LearningEffectiveDynamics Framework to learn effective dynamics and couple a macro scale simulator...	20	Experimental	11	Python
100	Shraddha22710/SKOOP-RED Official code for the IEEE SPL paper "Stabilizing RED using the Koopman...	19	Experimental	2	Jupyter Notebook
101	junetroan/Deep-Learning-Strategies Code developed for the authors master's thesis "Novel Deep Learning...	19	Experimental	3	Julia
102	enochkan/kalmanpy Implementation of Kalman Filter in Python	18	Experimental	36	Python
103	benettia/phaseflux Ever wondered what happens when gas and liquid mix inside a tube?	17	Experimental	—	Python
104	Northeastern-Research-ORNL-1/pyreflect-interface A minimal, monochrome web interface for the pyreflect neutron reflectivity...	17	Experimental	1	Python
105	LeiMinghaoSJTU/neural-operators 深度学习求解PDE：神经算子中文示例Notebook	15	Experimental	2	Jupyter Notebook
106	dantor03/daudin-delarue-moons Empirical verification of Daudin & Delarue (2025): mean-field Neural ODEs...	14	Experimental	—	Python
107	Zylus08/Neural-Surrogate-Monte-Carlo-Collision-Simulator Hybrid Monte Carlo + Neural surrogate simulator for high-energy particle...	14	Experimental	—	TypeScript
108	LaoZhongjie/lstm-chaos-dynamics A research project investigating how LSTM training dynamics relate to...	14	Experimental	—	Python
109	Lingkai-Kong/so-ebm Code for paper: End-to-end Stochastic Optimization with Energy-based Model	14	Experimental	16	Python
110	EdWangLoDaSc/DSOVT Sample codes for training of dynamical system prediction from sparse...	12	Experimental	6	Jupyter Notebook
111	mschossler/fluctuationRelations Fluctuations are important for systems with a small number of degrees of...	11	Experimental	—	—

Comparisons in this category

torchsde and torchcde (62 vs 55)