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This work presents a novel algorithm that integrates a data-efficient function approximator with reinforcement learning in continuous state spaces. An online and incremental algorithm capable of learning from a single pass through data,…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In…
There are quantum algorithms for finding a function $f$ satisfying a set of conditions, such as solving partial differential equations, and these achieve exponential quantum speedup compared to existing classical methods, especially when…
Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
We motivate the use of neural networks for the construction of numerical solutions to differential equations. We prove that there exists a feed-forward neural network that can arbitrarily minimise an objective function that is zero at the…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the…
As is well known, both sampling from the posterior and computing the mean of the posterior in Gaussian process regression reduces to solving a large linear system of equations. We study the use of stochastic gradient descent for solving…
While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected…
We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…
The particle filter (PF) and the ensemble Kalman filter (EnKF) are widely used for approximate inference in state-space models. From a Bayesian perspective, these algorithms represent the prior by an ensemble of particles and update it to…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
A method to increase the precision of feedforward networks is proposed. It requires a prior knowledge of a target function derivatives of several orders and uses this information in gradient based training. Forward pass calculates not only…