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This paper identifies a consistent three-regime structure in scientific machine learning models, showing that optimization effectiveness is regime-specific and can challenge conventional loss-landscape interpretations. It proposes a regime-aware diagnostic framework validated across PINNs, neural operators, and neural ODEs.
The paper introduces beignet, a PINN architecture that replaces random Fourier features with a trainable multi-resolution Fourier feature pyramid, achieving higher accuracy and computational efficiency on PDE benchmarks.
This paper introduces a novel uncertainty-aware PINN framework for flood inference from SAR data, addressing 'physics shock' by dynamically relaxing physical constraints in noisy regions. Evaluated on Sen1Floods11, the method achieves a 25% improvement in IoU and provides calibrated uncertainty bounds for operational disaster response.
This paper presents a physics-informed convolutional encoder–decoder network to predict pore-scale velocity fields from porous media geometry, and demonstrates that using network predictions to initialize Lattice-Boltzmann simulations accelerates convergence in over 90% of cases.
This paper proposes a spatially correlated curriculum learning framework for Physics-Informed Neural Networks (PINNs) that improves training stability and solution accuracy by leveraging spatial correlations among subregions, addressing issues like high-dimensional non-convex loss landscapes and imbalanced multi-objective constraints.
Met-Shield is an open-source re-entry simulator that uses a Physics-Informed Neural Network (PINN) to predict thermal gradients on a spacecraft shield, integrated into a C++ WebAssembly engine for real-time browser performance. The project addresses robustness over traditional solvers but faces convergence issues during high heat flux phases.
This paper introduces 'Data-Guided FVM-PINN', a framework using finite-volume losses for 2D shallow water equations, demonstrating that sparse data guidance is crucial to prevent network collapse in rugged loss landscapes.
This paper introduces Geometric Kolmogorov-Arnold Networks (GeoKAN), a family of geometry-aware models that learn Riemannian metrics to adapt coordinates for improved function approximation and physics-informed learning.
This paper proposes a self-supervised physics-informed neural network (PINN) framework with a learnable blending neuron to adaptively balance physics-based and data-driven losses, and integrates transfer learning to improve efficiency under data scarcity. It is validated on liquid-metal miniature heat sink CFD data with only 87 datapoints, achieving under 8% error.