相关论文: Solving for high dimensional committor functions u…

The distribution system problems, such as planning, loss minimization, and energy restoration, usually involve the phase balancing or network reconfiguration procedures. The determination of an optimal phase balance is, in general, a…

We present a novel yet simple deep learning approach, called input gradient annealing neural network (IGANN), for solving stationary Fokker-Planck equations. Traditional methods, such as finite difference and finite elements, suffer from…

Transport through nanosystems is treated within the second order von Neumann approach. This approach bridges the gap between rate equations which neglect level broadening and cotunneling, and the transmission formalism, which is essentially…

We consider statistical inference for parameters defined by general estimating equations under the covariate shift transfer learning. Different from the commonly used density ratio weighting approach, we undertake a set of formulations to…

We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…

In this paper we present an adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P) equations. F-P equations are usually high-dimensional and defined on an unbounded domain,…

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…

In this paper we analyze the global existence of classical solutions to the initial boundary-value problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a…

Any strategy used to distribute a robot ensemble over a set of sequential tasks is subject to inaccuracy due to robot-level uncertainties and environmental influences on the robots' behavior. We approach the problem of inaccuracy during…

Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…

Understanding the transition events between metastable states in complex systems is an important subject in the fields of computational physics, chemistry and biology. The transition pathway plays an important role in characterizing the…

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…

The convergence properties of the stationary Fokker-Planck algorithm for the estimation of the asymptotic density of stochastic search processes is studied. Theoretical and empirical arguments for the characterization of convergence of the…

A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…

Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…

Neural networks are often regarded as "black boxes" due to their complex functions and numerous parameters, which poses significant challenges for interpretability. This study addresses these challenges by introducing methods to enhance the…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…

Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…