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Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We propose an intuitive, machine-learning approach to multiparameter inference, dubbed the InferoStatic Networks (ISN) method, to model the score and likelihood ratio estimators in cases when the probability density can be sampled but not…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

We propose two generic methods for improving semi-supervised learning (SSL). The first integrates weight perturbation (WP) into existing "consistency regularization" (CR) based methods. We implement WP by leveraging variational Bayesian…

Scientific modeling faces a tradeoff between the interpretability of mechanistic theory and the predictive power of machine learning. While existing hybrid approaches have made progress by incorporating domain knowledge into machine…

The objective of this work is to quantify the uncertainty in probability of failure estimates resulting from incomplete knowledge of the probability distributions for the input random variables. We propose a framework that couples the…

Bayesian Likelihood-Free Inference methods yield posterior approximations for simulator models with intractable likelihood. Recently, many works trained neural networks to approximate either the intractable likelihood or the posterior…

In simulations of multiscale dynamical systems, not all relevant processes can be resolved explicitly. Taking the effect of the unresolved processes into account is important, which introduces the need for paramerizations. We present a…

In the era of big data, machine learning (ML) has become a powerful tool in various fields, notably impacting structural dynamics. ML algorithms offer advantages by modeling physical phenomena based on data, even in the absence of…

Statistical Relational Learning (SRL) methods for anomaly detection are introduced via a security-related application. Operational requirements for online learning stability are outlined and compared to mathematical definitions as applied…

Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in…

Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize…

Both uncertainty estimation and interpretability are important factors for trustworthy machine learning systems. However, there is little work at the intersection of these two areas. We address this gap by proposing a novel method for…

Bayesian neural networks offer better estimates of model uncertainty compared to frequentist networks. However, inference involving Bayesian models requires multiple instantiations or sampling of the network parameters, requiring…

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…

Simulation-based inference (SBI) methods typically require fully observed data to infer parameters of models with intractable likelihood functions. However, datasets often contain missing values due to incomplete observations, data…

Statistical divergences (SDs), which quantify the dissimilarity between probability distributions, are a basic constituent of statistical inference and machine learning. A modern method for estimating those divergences relies on…

Simulation-Based Inference (SBI) offers a principled and flexible framework for conducting Bayesian inference in any situation where forward simulations are feasible. However, validating the accuracy and reliability of the inferred…

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Leading uncertainty…