H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
Respecting causality is all you need for training physics-informed neural networks
9 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.
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.
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.
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.
citing papers explorer
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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
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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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The Design and Composition of Structural Causal Decision Processes
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.
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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.
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Physics-Informed Neural Networks for Solving Derivative-Constrained PDEs
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.
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Enabling Structure-Only Initialization and Out-of-Distribution Generalization in GNN-based Molecular Dynamics Simulators
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.
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Differentiable Chemistry in PINNs for Solving Parameterized and Stiff Reaction Systems
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.
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PINNACLE: An Open-Source Computational Framework for Classical and Quantum PINNs
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.