Wave Function Backpropagation (WFB) introduces a wave‑parameterized learning framework where neural responses are described by amplitude, wavenumber, angular frequency, and phase, linking each observed state to its temporal interval Δt via the wave’s phase. The authors derive standard WFB gradients and a spatial‑curvature correction using the Laplacian of the wave response, and instantiate WFB in a feed‑forward trajectory predictor. Experiments show that using real intervals reduces average displacement error (ADE) by 20.4% over a baseline FFN, and that WFB remains competitive with ReLU controls, demonstrating its viability as a structured feed‑forward learning formulation.
Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniforml...
The paper introduces the Spatiotemporal Conditional Operator (STCO), a framework for learning neural operators that can incorporate prescribed target‑time condition fields—such as body motion, inflow disturbances, or body‑force actuation—into time‑dependent PDE simulations. STCO combines a Flow‑Aware Graph Leaf (FAGL) partitioning scheme with Dual‑Site Feature‑wise Linear Modulation (DSFiLM) to inject these conditions before and after the core operator computation. Evaluated on twelve backbone architectures across an immersed‑boundary CFD benchmark, STCO achieves significant reductions in relative‑L2 field error (31.1%) and pressure‑derived load error (24.7%) while improving long‑lead predictions for most backbones.
arXiv:2609. 19039v1 Announce Type: cross Abstract: We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics.
The paper introduces the Frequency Selective Neural Network (FSNN), a new foundation architecture for time‑series learning that embeds advanced signal‑processing mathematics into its neural topology. By using a fully differentiable Wiener‑like filter bank optimized with complex‑domain backpropagation, FSNN autonomously discovers and isolates the precise physical modes of a given task, thereby avoiding the spectral entanglement that plagues CNNs, RNNs, and Transformers. Extensive evaluations show that FSNN achieves state‑of‑the‑art predictive performance, attaining 77.0 % average accuracy on the 10 multivariate UEA datasets and leading all major metrics on the imbalanced PTB‑XL ECG benchmark, while converging directly on physically meaningful frequency bands such as the cardiac QRS complex.
arXiv:2606. 16575v1 Announce Type: new 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: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.
ROMNet is a hybrid reduced‑order modeling and machine‑learning framework designed to improve waveform inversion for acoustic waves. It replaces the costly nonlinear mapping from a reduced‑order model (ROM) matrix to wave speed with a neural network that outputs a simpler ROM matrix, thereby reducing computational effort. The method is validated on two training datasets—random Gaussian‑based media and the GeoFWI benchmark—and compared against direct ROM inversion and two deep‑learning FWI approaches, Fourier‑DeepONet and InversionNet.
arXiv:2602. 18131v2 Announce Type: replace Abstract: Temporal Predictive Coding provides a layer-local, parallelisable mechanism for learning in recurrent systems, making it an attractive candidate for online local learning on neuromorphic and edge hardware.
The paper introduces a simplified Physics-Informed Neural Network (PINN) that uses trainable Gabor basis functions to better capture the localized, oscillatory nature of acoustic wavefields, addressing the low‑frequency bias of traditional PINNs. By redefining the network’s task as learning a nonlinear mapping to a custom Gabor coordinate system, the method absorbs Gabor parameters into the mapping, reducing computational complexity and eliminating manual hyperparameter tuning. Numerical experiments on various velocity models demonstrate faster convergence, higher accuracy, and greater robustness compared to conventional PINNs and earlier Gabor‑based approaches, with the implementation made publicly available for reproducibility.
arXiv:2607. 18830v1 Announce Type: cross Abstract: Model-Agnostic Meta-Learning (MAML) is a widely used framework for reinforcement learning (RL) that enables efficient transfer by learning global policy parameters that can be rapidly adapted to new tasks.
arXiv:2606. 09756v1 Announce Type: new Abstract: Responses to perturbations are key to understanding physical systems.
arXiv:2606. 13302v1 Announce Type: new Abstract: Wave parameters in the nearshore are crucial for coastal engineering, shoreline protection, marine hazard assessment, and coastal management for climate resilience.