“You throw a ball up (or at an angle), and note down the height of the ball at different points of time.”

“By embedding the Riemannian metric tensor into the automatic differentiation graph, our architecture analytically reconstructs the Laplace-Beltrami operator, decoupling solution complexity from geometric discretization.”

“BatteryAgent effectively corrects misclassifications on hard boundary samples, achieving an AUROC of 0.986, which significantly outperforms current state-of-the-art methods.”

“Classical approaches retain high-order accuracy and strong computational efficiency for single-instance problems... Physics-informed neural networks (PINNs) are also able to reproduce qualitative solutions but are generally less accurate and less efficient in low dimensions than classical solvers.”

“The paper introduces Energy-Aware Bayesian-CBFs (EB-CBFs) that construct conservative energy-based barriers directly from the Hamiltonian and vector-field posteriors, yielding safety filters that minimally modify a nominal controller while providing probabilistic energy safety guarantees.”

“PINNs run 90,000 times slower than finite difference with larger errors.”

“The method couples a high-fidelity, asymptotic-preserving VPL solver with inexpensive, strongly correlated surrogates based on the Vlasov--Poisson--Fokker--Planck (VPFP) and Euler--Poisson (EP) equations.”

“TPI-AI outperforms standalone LightGBM and Bi-LSTM baselines, achieving macro-F1 of 0.9562, 0.9124, 0.8345 on highD and 0.9247, 0.8197, 0.7605 on exiD at T = 1, 2, 3 s, respectively.”

“PhyAVBench explicitly evaluates models' understanding of the physical mechanisms underlying sound generation.”

“DUALFloodGNN achieves substantial improvements in predicting multiple hydrologic variables while maintaining high computational efficiency.”

“The resulting augmented excess free-energy functional quantitatively reproduces equilibrium density profiles, coexistence curves, and surface tensions across a broad temperature range, and accurately predicts contact angles and droplet shapes far beyond the training regime.”

“NeuroSPICE's flexibility enables the simulation of emerging devices, including highly nonlinear systems such as ferroelectric memories.”

“The study demonstrates hybrid training strategies can bring PINNs closer to FDTD-level accuracy and energy consistency.”

“The boundary function $B(\vec{x})$ functions as a spectral filter, reshaping the eigenspectrum of the neural network's native kernel.”

“MUSIC accurately learns solutions to complex coupled systems under data-scarce and noisy conditions, consistently outperforming non-sparse formulations.”

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“PI-MFM consistently outperforms purely data-driven counterparts, especially with sparse labeled spatiotemporal points, partially observed time domains, or few labeled function pairs.”

“The residual PINN with sinusoidal activations achieves the highest accuracy for both interpolation and extrapolation of RIRs.”

“FluenceFormer with Swin UNETR achieves the strongest performance among the evaluated models and improves over existing benchmark CNN and single-stage methods, reducing Energy Error to 4.5% and yielding statistically significant gains in structural fidelity (p < 0.05).”

“LD-DIM achieves consistently improved numerical stability and reconstruction accuracy of both parameter fields and corresponding PDE solutions compared with physics-informed neural networks (PINNs) and physics-embedded variational autoencoder (VAE) baselines, while maintaining sharp discontinuities and reducing sensitivity to initialization.”

“Results demonstrate how learned attack policies disrupt load balancing and induce voltage instabilities that propagate across T and D boundaries.”

“The matrix closest to $\widehat{A}$ in the Frobenius norm and satisfying $C^ op A = 0$ is the orthogonal projection $A^\star = \widehat{A} - C(C^ op C)^{-1}C^ op \widehat{A}$.”

“Incorporating cosmic-ray information further improves 48-hour forecast skill by up to 25.84% (from 0.178 to 0.224).”

“The model shows consistent and improved performance, having been trained on a dataset of 2112 inorganic materials with validated phonon spectra, and getting an F1-score of 0.83 for both stable and unstable classes.”

“The research focuses on the prediction of steady-state electrohydrodynamic flow.”

“To overcome this limitation, our framework requires only the computation of directional derivatives and a pre-basis for the Hilbert space domain.”

“The article likely details the methodology, results, and potential implications of using physics-informed diffusion models for RSRP prediction.”

“The article is sourced from ArXiv, indicating it is likely a pre-print research paper.”

“The article's context revolves around the study from ArXiv, focusing on the paradoxical effect of constraint removal in physics-informed machine learning.”

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“FusionNet leverages trainable signal-processing priors.”

“The article is from ArXiv, a pre-print server, indicating preliminary research.”

“The article focuses on Part I: Basic Concepts, Neural Networks, and Variants.”

“The research focuses on Physics-Informed Neural Networks and Uncertainty Quantification.”

“The paper focuses on improving the consistency of accuracy.”

“The research focuses on using Physics-Informed Diffusion Models for MRI.”

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“The research is sourced from ArXiv, a repository for scientific preprints.”

“CARONTE is a Physics-Informed Extreme Learning Machine-Based Algorithm for Plasma Boundary Reconstruction.”

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“The research focuses on using physics-informed neural operators.”

“PIP$^2$ Net is presented.”

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“Physics-Informed Neural Networks with Adaptive Constraints for Multi-Qubit Quantum Tomography”

“The research focuses on error bound analysis.”

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“The research focuses on ultra-low-latency real-time neural PDE solvers.”

“The article's context revolves around rethinking physics-informed regression.”

“The research focuses on optimal execution using physics-informed neural networks.”