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Background: Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, and healthcare informatics. They are used to simulate complex dynamic…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Part-prototype Networks (ProtoPNets) are concept-based classifiers designed to achieve the same performance as black-box models without compromising transparency. ProtoPNets compute predictions based on similarity to class-specific…

Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

We study the problem of finite-horizon probabilistic invariance for discrete-time Markov processes over general (uncountable) state spaces. We compute discrete-time, finite-state Markov chains as formal abstractions of general Markov…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

In this paper we propose a novel human-centered approach for detecting forgery in face images, using dynamic prototypes as a form of visual explanations. Currently, most state-of-the-art deepfake detections are based on black-box models…

A representation of the cause-effect mechanism is needed to enable artificial intelligence to represent how the world works. Bayesian Networks (BNs) have proven to be an effective and versatile tool for this task. BNs require constructing a…

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time…

Deep neural networks (DNNs) have become ubiquitous thanks to their remarkable ability to model complex patterns across various domains such as computer vision, speech recognition, robotics, etc. While large DNN models are often more…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Differential networks (DN) are important tools for modeling the changes in conditional dependencies between multiple samples. A Bayesian approach for estimating DNs, from the classical viewpoint, is introduced with a computationally…

We describe a novel scheme for analyzing particle detector measurements when a well-calibrated, similarly instrumented spacecraft is present in a similar orbit. To prepare ground truth from measurements provided by a reference spacecraft,…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

One of the major challenges in machine learning nowadays is to provide predictions with not only high accuracy but also user-friendly explanations. Although in recent years we have witnessed increasingly popular use of deep neural networks…

The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead,…

The lack of transparency of Deep Neural Networks continues to be a limitation that severely undermines their reliability and usage in high-stakes applications. Promising approaches to overcome such limitations are Prototype-Based…