Neural networks with change-of-variables and mesh-based losses outperform a deconvolution baseline in accuracy and speed for 2D finite-source reflector design on four benchmarks.
Gauss-newton natural gradient descent for physics- informed computational fluid dynamics.arXiv preprint arXiv:2402.10680
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The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.
Preconditioned gradient descent mitigates spectral bias and reduces grokking delays by enabling uniform parameter space exploration in the NTK regime, confirming grokking as a transition to the rich regime.
citing papers explorer
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Neural-network methods for two-dimensional finite-source reflector design
Neural networks with change-of-variables and mesh-based losses outperform a deconvolution baseline in accuracy and speed for 2D finite-source reflector design on four benchmarks.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
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Natural gradient descent with momentum
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.
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On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime
Preconditioned gradient descent mitigates spectral bias and reduces grokking delays by enabling uniform parameter space exploration in the NTK regime, confirming grokking as a transition to the rich regime.