Related papers: Neural Network-Based Parameter Estimation for Non-…

For Deep Neural Networks (DNNs) to become useful in safety-critical applications, such as self-driving cars and disease diagnosis, they must be stable to perturbations in input and model parameters. Characterizing the sensitivity of a DNN…

We study an alternative use of machine learning. We train neural nets to provide the parameter estimate of a given (structural) econometric model, for example, discrete choice or consumer search. Training examples consist of datasets…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

Deep Neural Networks (DNNs) have already become a crucial computational approach to revealing the spatial patterns in the human brain; however, there are three major shortcomings in utilizing DNNs to detect the spatial patterns in…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

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…

Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…

Decentralized optimization is critical for solving large-scale machine learning problems over distributed networks, where multiple nodes collaborate through local communication. In practice, the variances of stochastic gradient estimators…

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…

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…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

There are several numerical models that describe real phenomena being used to solve complex problems. For example, an accurate numerical breast model can provide assistance to surgeons with visual information of the breast as a result of a…

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…

This paper proposes two projector-based Hopfield neural network (HNN) estimators for online, constrained parameter estimation under time-varying data, additive disturbances, and slowly drifting physical parameters. The first is a…

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

A Deep Neural Network (DNN) based algorithm is proposed for the detection and classification of faults in industrial plants. The proposed algorithm has the ability to classify faults, especially incipient faults that are difficult to detect…

We consider the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in a wireless sensor network (WSN), where each sensor receives a single snapshot of the field. We assume that the observation…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…