The paper proposes a physics-informed neural network (PINN) architecture that uses the complex exponential function as an activation, producing sine and cosine outputs. Compared to standard sine-activated multilayer perceptrons, this design yields markedly better temperature reconstructions from sparse velocity data in cubic Rayleigh-Bénard convection, while keeping per‑step computational cost similar. The authors attribute the gains to the network’s ability to propagate both sine and cosine components, allowing each neuron in the next layer to adjust the phase of the latent periodic signals.
arXiv:2607. 02088v1 Announce Type: new Abstract: We propose an improved Fourier Neural Operator (FNO) for modeling two-dimensional Rayleigh-B\'enard convection by predicting time increments instead of full solutions, achieving higher accuracy than a standard FNO baseline.
arXiv:2606. 04582v1 Announce Type: cross Abstract: Real-time monitoring of the temperature distribution within components and sub-structures is a challenging topic in many systems due to restrictions on feasible sensor locations.
arXiv:2609.07983v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a promising approach for solving Partial Differential Equations (PDEs), offering a me...
arXiv:2607. 03682v1 Announce Type: cross Abstract: Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized.
arXiv:2606. 17659v1 Announce Type: new Abstract: This study introduces enhancements to physics-constrained neural networks (PCNNs) that improve the accuracy and stability of hybrid short-term weather forecasting models.
arXiv:2608. 14733v1 Announce Type: cross Abstract: Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using $\cos$, $\sin$, or a combination of both.
arXiv:2606. 28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data.
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
arXiv:2606. 16575v2 Announce Type: replace Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.
arXiv:2607. 14855v1 Announce Type: cross Abstract: We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations.
Physics-enriched neural solvers for transient ice-flow simulation present a method where a neural network represents the glacier velocity field, warm-started from the previous time step and updated with few optimizer iterations. By feeding the network inexpensive input fields derived from low-order ice-flow balances, the solver improves robustness and accuracy across three real-world glacier configurations, achieving surface-velocity errors reduced by factors of two to four at fixed runtime. The approach enables a 300-year Aletsch simulation to finish in under one minute on a single GPU, demonstrating significant computational savings compared to traditional higher-order models.
arXiv:2608. 19632v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) embed governing partial differential equations directly into the training loss, offering a promising alternative to costly CFD solvers for unsteady flows.