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.
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When and why pinns fail to train: A neural tangent kernel perspective.Journal of Computational Physics, 449:110768
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Update direction selection for PINN training is cast as a Chebyshev-center problem in the dual cone, yielding an efficient dual formulation with nonconvex convergence guarantees and automatic recovery of scale robustness and simultaneous descent.
Proves H^{-1} norm equivalence to expectation over random test functions and introduces SV-PINNs that outperform standard PINNs on eight elliptic problems.
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.
MC² corrects low-budget Monte Carlo solutions for elliptic PDEs with a single-pass neural network to match the accuracy of 1000× more Monte Carlo samples while outperforming classical and learned baselines.
A decoupled parametric PINN with conditional modulation and Rosenthal-derived output scaling achieves zero-shot thermal inference across arbitrary metal alloys in laser powder bed fusion.
A meta-network learns to adapt Gaussian basis geometry across parametric PDE families, which a physics-informed least-squares corrector then refines for improved accuracy.
ResearchEVO automates the discover-then-explain cycle by evolving algorithms via fitness-driven LLM co-evolution and generating grounded, anti-hallucination research papers through sentence-level RAG.
DLDMF disentangles latent dynamics for parameterized PDEs by feeding parameters into a latent embedding that initializes a parameter-conditioned Neural ODE, then uses dynamic manifold fusion with a shared decoder to reconstruct spatiotemporal fields for better generalization and extrapolation.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
A single-layer architecture called FlowMixer uses constrained matrix operations and a semi-group property to enable depth-agnostic, interpretable spatiotemporal forecasting with direct eigenmode extraction.
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