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The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…

Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this…

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes…

Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the…

Despite their success and widespread adoption, the opaque nature of deep neural networks (DNNs) continues to hinder trust, especially in critical applications. Current interpretability solutions often yield inconsistent or oversimplified…

This paper is motivated by studies in neuroscience experiments to understand interactions between nodes in a brain network using different types of data modalities that capture different distinct facets of brain activity. To assess…

Effective control requires knowledge of the process dynamics to guide the system toward desired states. In many control applications this knowledge is expressed mathematically or through data-driven models, however, as complexity grows…

Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the…

Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Modeling inter-dependencies between time-series is the key to achieve high performance in anomaly detection for multivariate time-series data. The de-facto solution to model the dependencies is to feed the data into a recurrent neural…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

Given high-dimensional time series data (e.g., sensor data), how can we detect anomalous events, such as system faults and attacks? More challengingly, how can we do this in a way that captures complex inter-sensor relationships, and…

Causal inference in a nonlinear system of multivariate timeseries is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world…

In contemporary scientific research, understanding the distinction between correlation and causation is crucial. While correlation is a widely used analytical standard, it does not inherently imply causation. This paper addresses the…

Event datasets are sequences of events of various types occurring irregularly over the time-line, and they are increasingly prevalent in numerous domains. Existing work for modeling events using conditional intensities rely on either using…