A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.
Rethinking the importance of sampling in physics-informed neural networks
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
representative citing papers
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation 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.
PINNs with hard and soft boundary enforcement solve membrane form-finding PDEs to accuracy comparable with FEM, with hard-BC yielding smaller boundary errors.
Empirical benchmarks indicate CViT-based PINOs with adapted PINN mitigations can match or exceed data-driven neural operators on parametric PDE tasks.
IR-PINNs improve long-time accuracy for evolution equations by enforcing integral constraints over time sub-intervals and using adaptive collocation point sampling.
Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.
citing papers explorer
-
Curriculum Learning of Physics-Informed Neural Networks based on Spatial Correlation
A spatially correlated curriculum learning framework for PINNs using causal weights, low-frequency bridges, and adaptive reweighting to reduce training failures on spatially coupled BVPs.
-
When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
-
Deep Learning Alternatives of the Kolmogorov Superposition Theorem
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
-
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.
-
Physics-informed neural networks for form-finding of unilateral membrane structures
PINNs with hard and soft boundary enforcement solve membrane form-finding PDEs to accuracy comparable with FEM, with hard-BC yielding smaller boundary errors.
-
On the training of physics-informed neural operators for solving parametric partial differential equations
Empirical benchmarks indicate CViT-based PINOs with adapted PINN mitigations can match or exceed data-driven neural operators on parametric PDE tasks.
-
Integral regularization PINNs for evolution equations
IR-PINNs improve long-time accuracy for evolution equations by enforcing integral constraints over time sub-intervals and using adaptive collocation point sampling.
-
A numerical study into neural network surrogate model performance for uncertainty propagation
Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.