Related papers: Studying First Passage Problems using Neural Netwo…
Implementations of spiking neural networks on neuromorphic hardware promise orders of magnitude less power consumption than their non-spiking counterparts. The standard neuron model for spike-based computation on such systems has long been…
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…
Large-scale neuromorphic architectures consist of computing tiles that communicate spikes using a shared interconnect. The communication patterns in such systems are inherently sparse, asynchronous, and localized due to the spiking nature…
We introduce DeepFHT, a survival-analysis framework that couples deep neural networks with first hitting time (FHT) distributions from stochastic process theory. Time to event is represented as the first passage of a latent diffusion…
In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…
The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…
The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…
Mathematical models of biological neural networks are associated to a rich and complex class of stochastic processes. In this paper, we consider a simple {\em plastic} neural network whose {\em connectivity/synaptic strength} $(W(t))$…
The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and…
Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time…
This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…
The simulation of partial differential equations is a central subject of numerical analysis and an indispensable tool in science, engineering and related fields. Existing approaches, such as finite elements, provide (highly) efficient tools…
In recent years, surrogate models based on deep neural networks (DNN) have been widely used to solve partial differential equations, which were traditionally handled by means of numerical simulations. This kind of surrogate models, however,…
In unsplittable network flow problems, certain nodes must satisfy a combinatorial requirement that the incoming arc flows cannot be split or merged when routed through outgoing arcs. This so-called "no-split no-merge" requirement arises in…
Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…
Fluidic injection provides a promising solution to improve the performance of overexpanded single expansion ramp nozzle (SERN) during vehicle acceleration. However, determining the injection parameters for the best overall performance under…
Imaging flow cytometry systems aim to analyze a huge number of cells or micro-particles based on their physical characteristics. The vast majority of current systems acquire a large amount of images which are used to train deep artificial…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…