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Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine…
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
This paper proposes an simple but yet effective approach to structured parametric controller design in a linear fractional form. The main contribution consists in using structured $\mathcal{H}_\infty$ oriented optimization tools in an…
Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…
In the signal processing and statistics literature, the minimum description length (MDL) principle is a popular tool for choosing model complexity. Successful examples include signal denoising and variable selection in linear regression,…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
Current control algorithms for aerial robots struggle with robustness in dynamic environments and adverse conditions. Model-based reinforcement learning (RL) has shown strong potential in handling these challenges while remaining…
Predicting and simulating aerodynamic fields for civil aircraft over wide flight envelopes represent a real challenge mainly due to significant numerical costs and complex flows. Surrogate models and reduced-order models help to estimate…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
A simulation environment of harbor maneuvers is critical for developing automatic berthing. Dynamic models are widely used to estimate harbor maneuvers. However, human decision-making and data analysis are necessary to derive, select, and…
A lubrication model describes the dynamics of a thin layer of fluid spreading over a solid substrate. But to make forecasts we need to supply correct initial conditions to the model. Remarkably, the initial fluid thickness is not the…
This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear…
In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior…
As an aid to the development of hydrogen separation membranes, we predict the temperature dependent phase diagrams using first principles calculations combined with thermodynamic principles. Our method models the phase diagram without…
We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system and its parameters, we modularize the design…