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This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for…
We propose to use neural networks to estimate the rates of coherent and incoherent processes in quantum systems from continuous measurement records. In particular, we adapt an image recognition algorithm to recognize the patterns in…
Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to…
Whether stochastic or parametric, the Pareto/NBD model can only be utilized for an in-sample prediction rather than an out-of-sample prediction. This research thus provides a neural network based extension of the Pareto/NBD model to…
We present a comprehensive evaluation of the robustness and explainability of ResNet-like models in the context of Unintended Radiated Emission (URE) classification and suggest a new approach leveraging Neural Stochastic Differential…
We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a…
The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…
There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…
Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…
Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…
We propose rigorous lower and upper error bounds for neural network (NN) approximations to PDEs by efficiently computing the Riesz representations of suitable extension and restrictions of the NN residual towards geometrically simpler…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled…
Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…
This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…