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- Generalization Error Analysis of Deep Backward Dynamic Programming for Solving Nonlinear PDEs
- An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains
- A mimetic discretization of Westervelt's equation
- Randomized Radial Basis Function Neural Network for Solving Multiscale Elliptic Equations
- Ultraspherical Spectral Method for Block Copolymer Systems on Unit Disk
- AP-MIONet: Asymptotic-preserving multiple-input neural operators for capturing the high-field limits of collisional kinetic equations
- Two-dimensional DtN-FEM scattering analysis of SH guided waves by an interface debonding in a double-layered plate
- Research on Real-time Diagnosis and Early Warning Technology of Automobile Faults Based on Fractional Order Differential Operator
- XI-DeepONet: An operator learning method for elliptic interface problems
- PFWNN: A deep learning method for solving forward and inverse problems of phase-field models
- Determining a Time-Varying Potential in Time-Fractional Diffusion from Observation at a Single Point
- Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions
- A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions
- Hybrid PDE-Deep Neural Network Model for Calcium Dynamics in Neurons
- Pseudo-Energy-Preserving Explicit Runge-Kutta Methods
- Hierarchical Alternating Least Squares Methods for Quaternion Nonnegative Matrix Factorizations
- Rapidly convergent series expansions for a class of resolvents
- Improving Greedy Algorithms for Rational Approximation
- High-order numerical method for solving elliptic partial differential equations on unfitted node sets
- Bernstein-von Mises theorems for time evolution equations
- Computing Stokes flows in periodic channels via rational approximation
- Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise
- Control of Instability in a Vlasov-Poisson System Through an External Electric Field
- Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces
- Cross-diffusion systems coupled via a moving interface
- Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties
- Finite Element Complexes in Two Dimensions
- Barycentric Interpolation Based on Equilibrium Potential
- Optimal approximation of infinite-dimensional holomorphic functions II: recovery from i.i.d. pointwise samples
- An efficient stochastic particle method for high-dimensional nonlinear PDEs
- Distributional Finite Element curl div Complexes and Application to Quad Curl Problems
- Generalised Adaptive Cross Approximation for Convolution Quadrature based Boundary Element Formulation
- A Higher-Order Multiscale Method for the Wave Equation
- Asymptotic spectral properties and preconditioning of an approximated nonlocal Helmholtz equation with Caputo fractional Laplacian and variable coefficient wave number $mu$
- Higher-Order Energy-Decreasing Exponential Time Differencing Runge-Kutta methods for Gradient Flows
- Energy-consistent Petrov-Galerkin time discretization of port-Hamiltonian systems
- Convergence of a Finite Volume Scheme for Compactly Heterogeneous Scalar Conservation Laws
- SOC-MartNet: A Martingale Neural Network for the Hamilton-Jacobi-Bellman Equation without Explicit inf H in Stochastic Optimal Controls
- About the Burton-Miller factor in the low frequency region
- Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems
- A Review of Neural Network Solvers for Second-order Boundary Value Problems
- Matrix perturbation bounds via contour bootstrapping
- A Payne-Whitham model of urban traffic networks in the presence of traffic lights and its application to traffic optimisation
- CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations
- Formalization of Complexity Analysis of the First-order Algorithms for Convex Optimization
- Convergence Analysis of Probability Flow ODE for Score-based Generative Models
- Open problems and perspectives on solving Friedrichs systems by Krylov approximation
- Physics-informed active learning with simultaneous weak-form latent space dynamics identification