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The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this…

The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…

Model-Driven Engineering (MDE) has seen significant advancements with the integration of Machine Learning (ML) and Deep Learning (DL) techniques. Building upon the groundwork of previous investigations, our study provides a concise overview…

The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…

High-throughput data generation methods and machine learning (ML) algorithms have given rise to a new era of computational materials science by learning relationships among composition, structure, and properties and by exploiting such…

Recent advancements in large language models (LLMs) have shown significant promise in various domains, especially robotics. However, most prior LLM-based work in robotic applications either directly predicts waypoints or applies LLMs within…

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…

In this thesis, we introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems, including online (continual) learning, prequential (one-step-ahead) forecasting, and contextual bandits. To…

In this chapter, we consider probabilistic drift-diffusion models and Bayesian inference frameworks to address this issue, assisting better social human decision-making. We provide details of the models, as well as representative numerical…

Determining a process-structure-property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials…

We introduce a closure model for wall-modeled large-eddy simulation (WMLES), referred to as the Building-block Flow Model (BFM). The foundation of the model rests on the premise that a finite collection of simple flows encapsulates the…

Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of…

By virtue of its great utility in solving real-world problems, optimization modeling has been widely employed for optimal decision-making across various sectors, but it requires substantial expertise from operations research professionals.…

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Large Language Models (LLMs) are increasingly applied in the fields of mechanical engineering and materials science. As models that establish connections through the interface of language, LLMs can be applied for step-wise reasoning through…

Existing LLM-enabled multi-agent frameworks are predominantly limited to digital or simulated environments and confined to narrowly focused knowledge domain, constraining their applicability to complex engineering tasks that require the…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

The convergence of artificial intelligence and materials science presents a transformative opportunity, but achieving true acceleration in discovery requires moving beyond task-isolated, fine-tuned models toward agentic systems that plan,…