PDE & Numerical Simulation

Scientific Machine Learning for PDEs
https://www.scimba.org/

NOEM: efficient and scalable finite element method enabled by reusable neural operators
https://www.nature.com/articles/s43588-026-00974-2

VisualPDE: Interactive Spatiotemporal Modeling via Web Browsers on Any Device
https://www.siam.org/publications/siam-news/articles/visualpde-interactive-spatiotemporal-modeling-via-web-browsers-on-any-device/

Functional Attention: From Pairwise Affinities to Functional Correspondences
https://arxiv.org/abs/2605.31559

TorchFSM Fourier Spectral Method with PyTorch
https://qiauil.github.io/torchfsm/

TensorMesh is a finite element method (FEM) library built on PyTorch
https://docs.tensor-mesh.com/

Mollifier Layers: Enabling Efficient High-Order Derivatives in Inverse PDE Learning
https://arxiv.org/abs/2505.11682

DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning
https://github.com/cruiseresearchgroup/DRIFT-Net

Geometric Neural Operators
https://github.com/atzberg/geo_neural_op

Fourier Neural Operators Explained: A Practical Perspective
https://arxiv.org/abs/2512.01421

Pinneaple - Unified Physical Data, Geometry, Models and Training for Physics AI
https://github.com/barrosyan/PINNeAPPle

Ultra Fast PDE Solving via Physics Guided Few-step Diffusion
https://arxiv.org/abs/2602.03627

Learning, Solving and Optimizing PDEs with TensorGalerkin
https://camlab-ethz.github.io/TensorGalerkin/

BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations
https://arxiv.org/abs/2602.14853

MFEM is a free, lightweight, scalable C++ library for finite element methods
https://mfem.org/

PI-MFM: Physics-informed multimodal foundation model for solving partial differential equations
https://arxiv.org/abs/2512.23056

Finite basis physics-informed neural networks
https://github.com/benmoseley/FBPINNs

PhysiX: A Foundation Model for Physics Simulations
https://github.com/ArshKA/PhysiX

Accelerating Porous Media Flow Simulations With Fourier Neural Operators: An Application to Geologic Storage of CO2
https://advanced.onlinelibrary.wiley.com/doi/abs/10.1002/adts.202500747

One-shot learning for solution operators of partial differential equations
https://www.nature.com/articles/s41467-025-63076-z

Thermodynamics-informed graph neural networks for real-time simulation of digital human twins
https://link.springer.com/article/10.1007/s00466-025-02633-1

Simulating a neural operating system with Gemini 2.5 Flash-Lite
https://developers.googleblog.com/en/simulating-a-neural-operating-system-with-gemini-2-5-flash-lite

Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics
https://arxiv.org/pdf/2509.08191

Training of physical neural networks
https://www.nature.com/articles/s41586-025-09384-2

Data-Driven Physical Simulations) seminars
https://www.librom.net/ddps.html

Flow Matching Meets PDEs: A Unified Framework for Physics-Constrained Generation
https://arxiv.org/abs/2506.08604

Anant-Net: Breaking the curse of dimensionality with scalable and interpretable neural surrogate for high-dimensional PDEs
https://www.sciencedirect.com/science/article/pii/S0045782525006759

Physics informed neural network framework for unsteady discretized reduced order system
https://www.sciencedirect.com/science/article/abs/pii/S0898122125001944

P3D: Scalable Neural Surrogates for High-Resolution 3D Physics Simulations with Global Context
https://arxiv.org/abs/2509.10186

PINNeAPPle - PINNFactory
https://github.com/barrosyan/pinnfactory