PDEBench
PDE Benchmark / Multi-Equation
Large-scale PDE benchmark covering heat, advection-diffusion and fluid dynamics - supports fair comparison of data-driven and physics-informed methods.
MIT License BenchmarkPDECFD
DClaw
A navigation hub for Physical AI and Scientific Machine Learning: systematically indexing five resource families — datasets & benchmarks, tools & frameworks, industrial cases, learning paths and papers & surveys — plus company research reports, a glossary, a weekly arXiv digest and a knowledge graph. Bilingual search and community submissions supported.
Browse Resources →🗃️ Datasets & Benchmarks
Training & evaluation datasets, scientific ML benchmarks
🧰 Tools & Frameworks
Solvers, training frameworks, post-processing & visualization tools
🎯 Applied Cases
Physics AI deployment cases in any domain - CAE, energy, weather, biomedicine, materials, geophysics and beyond
🎓 Learning Paths
Resources from beginner to industrial deployment
📄 Papers & Surveys
Must-read benchmark papers and technical surveys (no news or industry reports)
Featured
The Well
Multiphysics / PDE - 16 Domains
Unified benchmark spanning 16 physical domains, dubbed the 'ImageNet moment of physical ML', with PyTorch API, pretrained baselines and HF streaming.
Per subset (mostly CC-BY / code MIT) MultiphysicsBenchmarkPyTorch
DeepXDE
PINN Starter Framework
The most beginner-friendly PINN framework, with excellent Chinese docs and TensorFlow/PyTorch backends - the top choice to start with physics-informed networks.
GNU Lesser General Public License v2.1 PINNBeginnerChinese Docs
OpenFOAM
General-Purpose CFD Solver
The de facto open-source CFD solver covering incompressible/compressible flow, heat transfer, multiphase and combustion - the workhorse for generating physics-AI training data.
GPL v3 CFDOpen SourceSolver
PhysicsNeMo
Solver / Training Framework
NVIDIA's physics-ML training framework (formerly Modulus) with PINN, neural operators and physics-constrained training - commercial-friendly, industry-first choice.
Apache-2.0 PINNNeural OperatorNVIDIA
GraphCast: Data-Driven Weather Forecasting
Weather / Large-Scale Physical Prediction
A graph neural network for medium-range weather prediction that outperforms conventional numerical weather prediction on many targets while running in minutes instead of hours.
arXiv preprint (copyright held by authors) WeatherGraph Neural NetworkForecasting
MACE-MP-0: A Universal Machine-Learned Interatomic Potential
Molecular Dynamics / ML Interatomic Potential
A general-purpose machine-learned interatomic potential built on an equivariant graph neural network, trained on 150k public inorganic crystals, that runs stable molecular dynamics out of the box for solids, liquids, gases and reactions, and can be fine-tuned to ab initio accuracy with only a handful of configurations.
MIT (code) / arXiv preprint Molecular DynamicsML PotentialEquivariant GNN
Physics-Based Deep Learning (Online Book)
Textbook / Systematic Course
A free online textbook from TU Munich covering physics + deep learning: differentiable physics, PINNs, neural operators and turbulence modeling, with runnable code.
CC BY-NC-SA 4.0 TextbookDifferentiable PhysicsPINN
Recent Updates
CFD Correction of Open Tip Clearance Flow in a Compressor Cascade Using VAE Latent Space Adaptation
CFD
Proposes a non-intrusive correction method using VAE latent space adaptation to reduce discrepancies between CFD predictions and experiments for open tip clearance flow in compressor cascades, trained on 166 parametrically sampled CFD total pressure loss fields.
New See LICENSE file CFD correctiontip clearance flowVAE
Leakage-Safe Machine Learning for Hydrogen Embrittlement Detection in 316L Stainless Steel: A Region-Held-Out Evaluation of Texture and Deep Features in SEM Micrographs
Materials
A region-held-out evaluation protocol for hydrogen embrittlement detection in 316L stainless steel, preventing data leakage from same specimen regions, comparing texture features vs deep learning for SEM micrograph classification.
New See LICENSE file Hydrogen EmbrittlementStainless SteelSEM Imaging
Parnassus for the CLD Detector: A Generative Machine-Learning Surrogate for Detector Simulation and Reconstruction at the FCC-ee
HEP
This high-energy physics work develops a Parnassus conditional flow matching surrogate for the CLD detector, emulating full detector simulation and event reconstruction to address computationally expensive collider studies.
New See LICENSE file High-energy physicsParticle detector simulationGenerative surrogate model
Deep-Learning Solvers and Surrogates for Infinity and p-Laplace Problems
ScientificML
This paper investigates neural network solvers for infinity and p-Laplace problems in nonlinear analysis, applying PINNs and DeepONets to 2D and 3D domains with p values ranging from 2 to 1000.
New See LICENSE file Infinity equationsp-Laplace equationsPhysics-informed neural networks
POPT: Physics-Informed Deep Learning for Phase-Only Positioning in Distributed MIMO
Electromagnetics
A physics-informed deep learning framework performs single-snapshot 3D phase-only positioning in narrowband phase-coherent distributed MIMO networks under two-ray electromagnetic propagation.
New See LICENSE file Physics-informed learningDistributed MIMOPhase-only positioning
Decision-Gated Surrogate-Assisted Stochastic Optimization with Independent High-Fidelity Certification for Photovoltaic Hosting-Capacity Planning
Power Systems
This paper develops a surrogate-assisted stochastic multiobjective framework for photovoltaic hosting-capacity planning, jointly optimizing penetration and total electrical loss under reliability constraints.
New See LICENSE file photovoltaic hosting capacitysurrogate modelingstochastic multiobjective optimization
Equation Discovery with Bayesian Tree-Adjoining Grammars
ScientificML
A Bayesian tree-adjoining grammar framework for equation discovery and structure identification in general nonlinear systems.
New See LICENSE file equation discoveryBayesian modelingtree-adjoining grammars
Coupled Meta-Adaptive Filtering for Active Noise Control Under Time-Varying Acoustic Paths
Acoustics
This paper applies meta-adaptive filtering to active noise control when acoustic paths vary over time, constructing physics-informed optimizer features from a secondary-path estimate to support online filter updates.
New See LICENSE file active noise controlmeta-adaptive filteringtime-varying acoustic paths
On the Limits of Univariate Deep Learning for Significant Wave Height Forecasting
Fluid Mechanics
This study evaluates five deep learning architectures for univariate significant wave height forecasting using buoy observations. Across a 47-buoy, 37-year evaluation corpus, the model families converge to nearly identical performance, with an between-family standard deviation of 0.0014 square meters.
New See LICENSE file significant wave height forecastingocean buoysdeep learning comparison
Architecture Acceleration of Machine Learning Gravitational Waveform Surrogate Models
Geophysics
This paper presents differentiable and hardware-accelerated implementations of the machine-learning surrogate models mlgw and mlgw-bns for gravitational-wave waveform modeling, enabling JIT compilation, vector parallelization, GPU acceleration, and automatic differentiation within JAX.
New See LICENSE file gravitational waveswaveform surrogate modelsGPU acceleration
Gradient Surgery for Physics-Informed Neural Networks
ScientificML
This paper studies gradient conflicts and multi-task optimization in Physics-Informed Neural Networks, with implications for more stable convergence in stiff and high-frequency partial differential equations.
New See LICENSE file Physics-Informed Neural NetworksGradient ConflictsMulti-Task Optimization
Conformal Symplectic Structure of Brinkman Penalisation for Structure-Preserving Operator Learning of Hamiltonian PDEs
ScientificML
Reveals compatibility conditions under which multi-symplectic Hamiltonian PDEs regularized by Brinkman-type penalization retain a multi-conformal symplectic structure, yielding exact local conservation laws for structure-preserving operator learning on complex geometries.
New See LICENSE file Hamiltonian PDEsBrinkman penalizationStructure-preserving learning
Popular keywords
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