“The framework demonstrates potential for retrievals of atmospheric, cloud and surface variables, providing information that can serve as a prior, initial guess, or surrogate for computationally expensive full-physics inversion methods.”

“The paper establishes error bounds for the reconstructed solution and the source term without requiring classical source conditions, and derives an expected convergence rate for the source error in a weaker topology.”

“The resulting acceptor layer achieves a striking Δn response time as short as 9 fs, approaching a single optical cycle, and is further tunable to sub-cycle timescales.”

“The paper introduces smooth cumulative- and inverse-cumulative-distribution-function ((I)CDF) timesteppers that evolve distributions rather than particles.”

“The paper's key finding is the development of a semiparametric framework for debiased inverse reinforcement learning that yields statistically efficient inference for a broad class of reward-dependent functionals.”

“The problem becomes ill-posed as the system transitions from the ballistic to the diffusive regime, characterized by the Knudsen number converging to zero.”

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

“The paper constructs a general class of unique solutions to certain matrix equations and derives several equivalent properties of W-weighted DMP and MPD inverses.”

“The paper proposes to leverage connections between proximal operators and Hamilton-Jacobi partial differential equations (HJ PDEs) to develop novel deep learning architectures for learning the prior.”

“The inverse of this intersection number is precisely the AdS double-copy kernel for the four-point open- and closed-string generating functions.”

“NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables.”

“The characteristic energy decay time exhibits a universal inverse scaling $τ_0 \propto ε^{-1.03 \pm 0.02}$ with the dissipation parameter $ε= 1 - e^2$.”

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

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“The exponent $n$ entering the probability $P_{ m SCO}\sim 10^{-n}$ has dimensions of inverse time: it is an energy barrier divided by the Planck constant, rather than a dimensionless tunnelling action.”

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

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“The combined analysis demonstrates that explainable AI(XAI) techniques can illuminate hidden failure modes, guide architectural refinements, and inform obstacle aware deployment strategies for learning based IK.”

“Uniqueness of the solution is established in two cases - the one-dimensional setting and the Gaussian case.”

“SGPS enables more accurate posterior sampling and reduces error accumulation, maintaining high reconstruction quality with fewer than 100 Neural Function Evaluations (NFEs).”

“The length of the plasma column exhibits an inverse relationship with the electron-neutral collision frequency, indicating the significance of collisional damping in the propagation of energetic electrons.”

“NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables... within a single optimization loop.”

“The paper aims to uniquely identify unknown spatial anomalies -- interpreted as zones of habitat degradation -- and their associated ecological parameters in multi-species predator-prey systems.”

“The article likely details the mathematical formulation of P-FABRIK, its implementation, and experimental validation. It would probably compare its performance with existing methods in terms of accuracy, speed, and robustness.”

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

“Instruction-following capabilities improve substantially (+46% to +75% in IFEval for Llama-3.2-1B and 3B models).”

“The paper demonstrates the reconstruction of short-range perturbations from scattering data in a linearized and finite-dimensional setting, along with a stability result.”

“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.”

“The paper constructs four automorphic forms on the complex ball and relates them to the inverse of the period map, ultimately expressing the iterated limit using the Lauricella hypergeometric series.”

“The study concerns the limit from Inverse Power Potential to Hard Sphere Boltzmann Equation.”

“By establishing a direct algebraic mapping between target scattering responses and the network's physical parameters, we transform the design process from iterative optimization into deterministic calculation.”

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“The method constructs a differentiable representation of the Quantum Chromodynamics (QCD) PV kernel and embeds it as a fixed, physics-preserving layer inside a neural network.”

“The lower triangular matrix $L_G$ and the upper triangular matrix $U_G$, generated by FSAI, are non-singular and non-negative. The diagonal entries of $L_GAU_G$ are positive and $L_GAU_G$, the preconditioned matrix, is a singular M-matrix.”

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“The research focuses on the fast simulation of the Zero Degree Calorimeter.”

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“The research focuses on an Inverse Scattering Inspired Fourier Neural Operator for Time-Dependent PDE Learning.”

“The article's context indicates it explores inverse problems under integral conditions for the generalized Korteweg-de Vries equation.”

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“The research leverages deep learning and transfer learning.”

“The article introduces the Sobolev Algorithm for Local Smoothness Analysis (SALSA).”

“The article focuses on combining multiple solvers through deep neural networks.”

“The paper focuses on reliability-targeted simulation.”

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