Related papers: Existence of dynamical low rank approximations for…
In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…
In this paper, we would like to consider the Cauchy problem for semi-linear $\sigma$-evolution equations with double structural damping for any $\sigma\ge 1$. The main purpose of the present work is to not only study the asymptotic profiles…
We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in…
In the empirical study of evolutionary algorithms, the solution quality is evaluated by either the fitness value or approximation error. The latter measures the fitness difference between an approximation solution and the optimal solution.…
In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of…
State-of-the-art neural networks can be trained to become remarkable solutions to many problems. But while these architectures can express symbolic, perfect solutions, trained models often arrive at approximations instead. We show that the…
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the…
In this paper, we consider the Cauchy problem for semi-linear wave equations with structural damping term $\nu (-\Delta)^2 u_t$, where $\nu >0$ is a constant. As being mentioned in [8,10], the linear principal part brings both the diffusion…
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is…
We investigate the temporal concatenation of sub-policies in Markov Decision Processes (MDP) with time-varying reward functions. We introduce General Dijkstra Search (GDS), and prove that globally optimal goal-reaching policies can be…
Reinforcement learning (RL) problems are fundamental in online decision-making and have been instrumental in finding an optimal policy for Markov decision processes (MDPs). Function approximations are usually deployed to handle large or…
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…
Recent advances in natural language processing, primarily propelled by Large Language Models (LLMs), have showcased their remarkable capabilities grounded in in-context learning. A promising avenue for guiding LLMs in intricate reasoning…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
We introduce an innovative approach that incorporates a Distributionally Robust Learning (DRL) approach into Cox regression to enhance the robustness and accuracy of survival predictions. By formulating a DRL framework with a Wasserstein…
We introduce two novel interpolatory dynamical low-rank (DLR) approximation methods for the efficient time integration of the Boltzmann-BGK equation. Both methods overcome limitations of classic DLR schemes based on orthogonal projections…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
This paper is concerned with the existence of optimal controls for backward stochastic partial differential equations with random coefficients, in which the control systems are represented in an abstract evolution form, i.e. backward…