Related papers: Accurate and Reliable Forecasting using Stochastic…

Uncertainty in biological neural systems appears to be computationally beneficial rather than detrimental. However, in neuromorphic computing systems, device variability often limits performance, including accuracy and efficiency. In this…

This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The…

We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the Stochastic Neural Network (SNN) with the DeepONet. By…

Despite stereo matching accuracy has greatly improved by deep learning in the last few years, recovering sharp boundaries and high-resolution outputs efficiently remains challenging. In this paper, we propose Stereo Mixture Density Networks…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

Evidence-based deep learning represents a burgeoning paradigm for uncertainty estimation, offering reliable predictions with negligible extra computational overheads. Existing methods usually adopt Kullback-Leibler divergence to estimate…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential…

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Motivated by the need to identify erroneous disparity assignments, various approaches for uncertainty and confidence estimation of dense stereo matching have been presented in recent years. As in many other fields, especially deep learning…

In this paper, we consider a numerical homogenization of the poroelasticity problem with stochastic properties. The proposed method based on the construction of the deep neural network (DNN) for fast calculation of the effective properties…

Accurate crowd simulation is crucial for public safety management, emergency evacuation planning, and intelligent transportation systems. However, existing methods, which typically model crowds as a collection of independent individual…

In recent years, advancements in deep learning have spurred the development of numerous models for Long-term Time Series Forecasting (LTSF). However, most existing approaches struggle to fully capture the complex and structured dependencies…

Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must…

Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the…

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be…

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

How to improve generative modeling by better exploiting spatial regularities and coherence in images? We introduce a novel neural network for building image generators (decoders) and apply it to variational autoencoders (VAEs). In our…