A PINN-derived analytical correction to the dissipation-production coefficient C_ε0 in a k-ε-b RANS model captures the Rayleigh-Taylor transition to turbulence by coupling dissipation to the Froude number and directed-to-total kinetic energy ratio.
J., Toscano, J
2 Pith papers cite this work, alongside 11 external citations. Polarity classification is still indexing.
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abstract
We investigate the learning dynamics of fully-connected neural networks through the lens of gradient signal-to-noise ratio (SNR), examining the behavior of first-order optimizers like Adam in non-convex objectives. By interpreting the drift/diffusion phases in the information bottleneck theory, focusing on gradient homogeneity, we identify a third phase termed ``total diffusion", characterized by equilibrium in the learning rates and homogeneous gradients. This phase is marked by an abrupt SNR increase, uniform residuals across the sample space and the most rapid training convergence. We propose a residual-based re-weighting scheme to accelerate this diffusion in quadratic loss functions, enhancing generalization. We also explore the information compression phenomenon, pinpointing a significant saturation-induced compression of activations at the total diffusion phase, with deeper layers experiencing negligible information loss. Supported by experimental data on physics-informed neural networks (PINNs), which underscore the importance of gradient homogeneity due to their PDE-based sample inter-dependence, our findings suggest that recognizing phase transitions could refine ML optimization strategies for improved generalization.
fields
physics.flu-dyn 2years
2026 2representative citing papers
PINN and adjoint-state methods reconstruct bottom topography and surface velocity from surface measurements in the shallow-water equations, with robustness to noise and sparsity on synthetic data.
citing papers explorer
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Learning Turbulence Closures with Physics-Informed Neural Networks for the Rayleigh-Taylor Transition to Turbulence
A PINN-derived analytical correction to the dissipation-production coefficient C_ε0 in a k-ε-b RANS model captures the Rayleigh-Taylor transition to turbulence by coupling dissipation to the Froude number and directed-to-total kinetic energy ratio.
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Estimating bottom topography in shallow water flows
PINN and adjoint-state methods reconstruct bottom topography and surface velocity from surface measurements in the shallow-water equations, with robustness to noise and sparsity on synthetic data.