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Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…

Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under…

Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation of modern scientific data analysis. Existing causal structure discovery algorithms either do not provide Type I error control or cannot scale…

The application of machine learning on tabular data in specialized domains is severely limited by data scarcity. While generative models offer a solution, traditional methods falter in low-data regimes, and recent Large Language Models…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Traditional model-based diagnosis relies on constructing explicit system models, a process that can be laborious and expertise-demanding. In this paper, we propose a novel framework that combines concepts of model-based diagnosis with deep…

Systems design processes are increasingly reliant on simulation models to inform design decisions. A pervasive issue within the systems engineering community is trusting in the models used to make decisions about complex systems. This work…

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…

Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…

We study residual dynamics learning for differentially flat systems, where a nominal model is augmented with a learned correction term from data. A key challenge is that generic residual parameterizations may destroy flatness, limiting the…

Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…

A new method for estimating structural equation models (SEM) is proposed and evaluated. In contrast to most other methods, it is based directly on the data, not on the covariance matrix of the data. The new approach is flexible enough to…