Proposes Interface Autoencoder (IAE) for learning neural operators on geometry-dependent PDEs, representing interface-function states in a fixed domain via finite projection codes.
A focused survey of PINN improvements via transfer learning and meta-learning, addressing PINN's notorious convergence difficulty and the need to re-optimize on every PDE parameter change - the engineering reference for productionizing PINNs.
arXiv preprint (copyright held by authors)PINNTransfer LearningMeta Learning
A systematic survey of physics-knowledge + ML methods for PDE prediction, splitting the field into architectural-level (loss, structured prediction, augmentation) and data-level (multi-task, meta, contextual) approaches, with industrial perspective and open-source ecosystem review.
arXiv preprint (copyright held by authors)Physics-informed MLPDEMulti-task Learning
Reframes Transolver's Physics-Attention as a special case of linear attention and proposes LinearNO (Linear Attention Neural Operator); achieves SOTA on six PDE benchmarks with 40.0% fewer parameters and 36.2% less compute, plus superior performance on AirfRANS and Shape-Net Car industrial datasets.
arXiv preprint (copyright held by authors)Neural OperatorTransformerLinear Attention
A joint training approach that addresses neural operator out-of-distribution degradation and PINN multi-solution convergence errors by leveraging imperfect neural operators to guide PINN optimization.
A provenance-bearing benchmark for verifying symbolic candidate solutions to PDEs, containing 20 records with generator outputs, verification cases, and human annotations for assessing symbolic solver reliability.
Proposes a physics-attention mechanism that projects meshes onto learnable physical-state tokens, improving efficiency and accuracy of PDE solving on large industrial geometries.
arXiv preprint (copyright held by authors)TransformerGeometryIndustrial
Introduces neural operators with integral kernels parameterized in Fourier space, enabling resolution-invariant PDE solving - a foundational and highly cited work in physics AI.
arXiv preprint (copyright held by authors)FNONeural OperatorFoundational
ETH Zurich's PDE foundation model and downstream fine-tuning suite, using semigroup augmentation to mine abundant training pairs, covering 15 downstream PDE tasks.
See LICENSE fileFoundation ModelNeural OperatorDownstream Tasks
Microsoft Research's open-source PDE benchmark suite with differentiable solvers and spatiotemporal dynamics data for evaluating long-horizon rollout stability.
DeepXDE v1.15.0 released with L-LAAF activation function support for JAX backend and Apple MPS GPU acceleration for PyTorch backend, improving deep learning-based PDE solving performance.
