220 papers
This paper establishes a maximum principle and the Hamilton-Jacobi-Bellman equation for optimal control on infinite-dimensional probability distribution spaces, and leverages these theoretical results to develop a scalable deep learning algorithm for solving high-dimensional multi-agent control problems.
This paper introduces Radial Müntz-Szász Networks (RMN), a highly parameter-efficient neural architecture that utilizes learnable radial power bases and a log-primitive to accurately model multidimensional singular fields like $1/r\log r$, achieving significantly lower error rates than standard MLPs and SIREN on benchmark tasks while providing closed-form gradients for physics-informed learning.
This paper proposes Graph-Instructed Neural Networks (GINNs) as a robust and scalable alternative to classical reduced order methods for efficiently simulating parametric partial differential equations with varying boundary conditions by learning the direct mapping between domain descriptions and PDE solutions.
This paper demonstrates that over-decaying step-size schedules in greedy sparse learning algorithms induce structural stagnation and prevent convergence in realizable regression problems, even in low-dimensional settings with controlled feature coherence.
This paper proposes the Latent Autoencoder Ensemble Kalman Filter (LAE-EnKF), a novel data assimilation method that learns a stable, linear state-space model in a latent space to overcome the performance limitations of standard EnKF on strongly nonlinear and chaotic systems while maintaining computational efficiency.
This paper presents a GPU-accelerated transient Electromagnetic-Thermal-Mechanical co-simulation solver that enables full-scale, non-homogenized early-stage design of advanced packages, overcoming the limitations of conventional steady-state methods by accurately capturing dynamic signal-induced stress and thermal events to prevent costly late-stage failures.
This paper proposes quantitative evaluation methods for assessing the stability and convergence of numerical solutions to the semilinear Klein–Gordon equation with power-law nonlinearity, while investigating optimal thresholds based on variations in initial value amplitude and mass.
This paper introduces Stochastic Physics-Informed Neural Networks (SPINNs) as a systematic deep learning framework for approximating solutions to stochastic differential equations driven by Lévy noise.
This paper establishes best approximation error estimates for discontinuous piecewise polynomial approximations in fractional Sobolev spaces on non-Lipschitz domains and meshes, even when the boundaries involved are fractal.
This paper presents a finite element discretization for elliptic distributed optimal control problems with boundary value tracking, reformulating the problem as a state-based variational form to derive optimal error estimates and fast solvers, which are validated through numerical experiments.
This paper proposes an Euler-type framework with equidistant step sizes for time-changed stochastic differential equations, establishing that both the standard and truncated Euler–Maruyama methods achieve strong convergence rates close to under global Lipschitz and relaxed Khasminskii-type conditions, respectively, which contrasts with the classical $1/2$ order found in methods using random step sizes.
This paper introduces two completely meshfree, high-order methods for integrating functions on arbitrary piecewise-smooth surfaces, including those with singular integrands, without requiring a curved mesh, initial triangulation, or increased point density near singularities.
This study introduces a physics-informed neural network (PINN) framework designed to accurately simulate fast bimolecular reactions in porous media, thereby enhancing the characterization of chemical interactions essential for critical mineral extraction and geoscience applications.
This paper proposes a stabilization-free General Order Virtual Element Method for Neumann boundary optimal control problems in saddle point formulation, providing rigorous a priori error estimates for arbitrary polynomial orders on general polygonal meshes and validating the approach through numerical experiments that demonstrate its effectiveness in avoiding stabilization parameter selection issues.
This paper establishes uniform regularity estimates for the principal Dirichlet eigenfunctions of both discrete random walks and continuous Brownian motion in Lipschitz domains by employing a novel probabilistic approach combining Feynman-Kac representations, gambler's ruin estimates, and a new "multi-mirror" coupling, while also reviewing convergence results between the discrete and continuous eigenfunctions.
The paper introduces the Mamba Neural Operator (MNO), a novel framework that bridges structured state-space models and neural operators to outperform Transformers in solving partial differential equations by more effectively capturing continuous dynamics and long-range dependencies.
This paper introduces the Block Sparse Tensor Train (BSTT) sketch, a structured random projection that unifies existing TT-adapted sketching operators and achieves linear scaling in tensor order and subspace dimension, thereby enabling quasi-optimal error bounds for tensor factorization and rounding tasks.
This paper establishes the first time-uniform error estimate for a fully discrete Luenberger observer applied to the one-dimensional barotropic Euler equations using mixed finite elements and implicit Euler time integration, demonstrating convergence that depends on initial errors, discretization parameters, and measurement noise via a modified relative energy technique.
This paper introduces a physics-informed neural particle method (PINN-PM) for the spatially homogeneous Landau equation that utilizes a continuous-time, mesh-free formulation to eliminate time-discretization errors, while providing rigorous stability analysis and error bounds that demonstrate superior accuracy and macroscopic invariant preservation compared to traditional time-stepping methods.
This paper establishes finite-horizon mean-square strong and weak error bounds for Euler--Maruyama simulations of current-based leaky integrate-and-fire networks by employing a path-space pruning-and-balance strategy that accounts for the unique concentration of numerical error at stochastic threshold-crossing events.