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Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves
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arXiv Machine Learning
Oct 8
Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves
Physics-informed neural PDE solvers typically keep a fixed representation while adapting parameters, which limits performance on heterogeneous problems. The authors propose physics-informed neural plasticity, allowing the representation itself to reshape during training. Their ReCAP method dynamically redistributes capacity via local enrichment, residual-directed splitting, gate-based pruning, and function-aware merging, achieving the lowest relative $L^2$ error on five challenging 3D and 4D benchmarks and reducing error by 10.7%–27.5% compared to the best competing solvers.
arXiv Machine Learning
Jun 3
Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv Machine Learning
Aug 26
Physics-Integrated Operator Learning via Gaussian Splatting Representations
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv Machine Learning
Aug 6
Continual-Learning Physics-Informed Neural Networks for Parameterized Partial Differential Equations
arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
arXiv Machine Learning
Jul 30
EvoPINN: Agentic Discovery of Executable Algorithms for Physics-Informed Neural Networks
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
arXiv AI
Sep 30
Transolver-$\sigma$: Joint Spectral-Physical Subspace Modeling for Neural PDE Solving
Transolver‑σ is a neural PDE solver that jointly models spectral and physical subspaces to improve accuracy in both one‑step and autoregressive rollouts. The method uses adaptive physical-state interactions, Slice‑Residual Physics‑Attention, and an axis‑factorized Fourier operator to enable information exchange between representations. Across five standard PDE benchmarks, Transolver‑σ reduces benchmark‑averaged relative error by 33.4% compared to the strongest baseline and shows strong performance on coupled multiphysics systems and real‑world fluid and combustion data.