Related papers: Solving for high dimensional committor functions u…
As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state, but also…
Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of…
Artificial intelligence (AI) has drawn significant inspiration from neuroscience to develop artificial neural network (ANN) models. However, these models remain constrained by the Von Neumann architecture and struggle to capture the…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics. In the paper, we introduce the Deep Neural Network (DNN) approximated solutions to the kinetic Fokker-Planck equation in a…
In this paper, we develop and analyze numerical methods for high dimensional Fokker-Planck equations by leveraging generative models from deep learning. Our starting point is a formulation of the Fokker-Planck equation as a system of…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
This work is concerned with solving high-dimensional Fokker-Planck equations with the novel perspective that solving the PDE can be reduced to independent instances of density estimation tasks based on the trajectories sampled from its…
Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive…
Ground robots which are able to navigate a variety of terrains are needed in many domains. One of the key aspects is the capability to adapt to the ground structure, which can be realized through movable body parts coming along with…
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task for quantum science. While several algorithms have been designed to solve those equations with…
We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…
It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [Science, 355(6325), 2017]. States…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
We introduce a model for an artificial neuron which is based on ballistic transport in a multi-terminal device. Unlike standard configurations, the proposed design embeds the synaptic weights into the active region, thus significantly…
Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…