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In this dissertation, we focus on several important problems in structured prediction. In structured prediction, the label has a rich intrinsic substructure, and the loss varies with respect to the predicted label and the true label pair.…

There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

The polynomial chaos (PC) expansion has been widely used as a surrogate model in the Bayesian inference to speed up the Markov chain Monte Carlo (MCMC) calculations. However, the use of a PC surrogate introduces the modeling error, that may…

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all…

Estimation of patient-specific model parameters is important for personalized modeling, although sparse and noisy clinical data can introduce significant uncertainty in the estimated parameter values. This importance source of uncertainty,…

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…

Solving complex problems requires continuous effort in developing theory and practice to cope with larger, more difficult scenarios. Working with surrogates is normal for creating a proxy that realistically models the problem into the…

One of the main challenges in surrogate modeling is the limited availability of data due to resource constraints associated with computationally expensive simulations. Multi-fidelity methods provide a solution by chaining models in a…

We present a new machine learning approach to estimate personalized treatment effects in the classical potential outcomes framework with binary outcomes. To overcome the problem that both treatment and control outcomes for the same unit are…

Machine learning surrogate emulators are needed in engineering design and optimization tasks to rapidly emulate computationally expensive physics-based models. In micromechanics problems the local full-field response variables are desired…

Most real-world optimization problems are difficult to solve with traditional statistical techniques or with metaheuristics. The main difficulty is related to the existence of a considerable number of local optima, which may result in the…

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

Multi-fidelity methods leverage low-cost surrogate models to speed up computations and make occasional recourse to expensive high-fidelity models to establish accuracy guarantees. Because surrogate and high-fidelity models are used…

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…

Urban infrastructure degrades over time, necessitating periodic renovation to maintain functionality and safety. When renovation is delayed beyond the infrastructure's remaining lifespan, costly emergency interventions become necessary to…