arXiv:2606. 19368v1 Announce Type: cross Abstract: In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations.
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. 02623v1 Announce Type: cross Abstract: Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2606. 08956v1 Announce Type: new Abstract: Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2606. 19853v1 Announce Type: new Abstract: We introduce SEA-PINN, a novel architecture that incorporates a Squeeze-Excitation-like attention mechanism into physics-informed neural networks to dynamically recalibrate the importance of neurons across layers.
arXiv:2607. 23466v1 Announce Type: new Abstract: Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited.
arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.
arXiv:2607. 16177v1 Announce Type: new Abstract: Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems.
arXiv:2511. 10101v2 Announce Type: replace Abstract: Background: both embodied intelligence and developmental morphogenesis depend on a division of labour between centralized guidance and distributed material dynamics, but the amount of top-down control needed to steer self-organization remains unclear.
arXiv:2606. 15271v1 Announce Type: cross Abstract: This work presents a transparent and reproducible benchmark study of a direct dual-network Physics-Informed Neural Network (PINN) formulation for the optimal control of a mass-spring-damper system.
arXiv:2608. 00097v1 Announce Type: cross Abstract: Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements.