Introduces pinn-gym benchmark demonstrating that low curve error in physics-informed surrogates frequently fails to yield useful design selections across per-material, pooled, and cross-material settings.
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Respectingcausality is all you need for training physics-informed neural networks
17 Pith papers cite this work. Polarity classification is still indexing.
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PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.
Proves H^{-1} norm equivalence to expectation over random test functions and introduces SV-PINNs that outperform standard PINNs on eight elliptic problems.
SCDMs and SCDPs are composable causal decision models that are strictly more expressive than POMDPs by allowing endogenous memory formation and variable discounting without rational belief assumptions.
A hybrid MRI-PINN-resolvent framework extracts mean fields from stenotic flow measurements and identifies stationary eigenmodes in the recirculation bubble plus broadband pseudo-resonance in the shear layer.
NSEM solves Poisson-Nernst-Planck benchmarks to 10^-4 to 10^-7 relative error using two orders of magnitude fewer collocation points than adaptive PINNs by combining spectral differentiation matrices with neural networks and a boundary-layer coordinate map.
WaveLiT combines wavelet tokenization, linear attention, and multiscale pyramids to produce parameter-efficient neural PDE solvers that match much larger models on TheWell benchmarks.
MetaColloc meta-learns a universal set of neural basis functions offline so that new PDEs can be solved at test time with a single linear solve instead of per-equation neural-network optimization.
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.
DC-PINNs embed derivative constraints into PINN optimization using a minimum principle and adaptive balancing, reducing violations and improving fidelity on heat, finance, and fluid benchmarks.
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
GNN-based MD simulators achieve stable structure-only initialization and reliable OOD generalization through inference-time physics optimization and a GNN barostat on elastic network compression tasks.
A differentiable chemistry solver is added to PINNs along with parameterized network architecture and stiffness-tailored residual weighting to solve initial/boundary value problems, inverse parameter identification, and parameterized PDEs for hydrogen combustion.
PINNACLE is an open-source framework for classical and quantum PINNs that supplies modular training methods and benchmarks showing high sensitivity to architecture choices plus parameter-efficiency gains in some hybrid quantum regimes.
A PIDL framework with shared-encoder architecture and Softplus constraints solves CSTR ODEs and financial inverse Fokker-Planck PDEs, claiming zero Second-Law violations and over 90% accuracy with 30% training data.
Trefftz-PINNs preserve the global topology of magnetic field lines and velocity streamlines more reliably than standard PINNs even when mean squared errors are matched.
citing papers explorer
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Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks
PINN gradient conflicts occur in distinct regimes (persistent directional, magnitude imbalance, or low/transient) that each favor different fixes, with per-loss adapters plus reweighting improving results on forward and multi-physics problems.
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MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions
MetaColloc meta-learns a universal set of neural basis functions offline so that new PDEs can be solved at test time with a single linear solve instead of per-equation neural-network optimization.
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Error whitening: Why Gauss-Newton outperforms Newton
Gauss-Newton descent whitens errors by projecting Newton directions or gradients onto the tangent space, replacing JJ^T with the identity and removing parameterization distortions that affect Newton descent.