Related papers: Data-Driven Nonlinear Model Reduction to Spectral …
The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…
Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…
The ability to robustly and efficiently control the dynamics of nonlinear systems lies at the heart of many current technological challenges, ranging from drug delivery systems to ensuring flight safety. Most such scenarios are too complex…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…
Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and…
Approximate dynamic programming has been investigated and used as a method to approximately solve optimal regulation problems. However, the extension of this technique to optimal tracking problems for continuous time nonlinear systems has…
We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…
Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…
We show how spectral submanifold theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predictions include an explicit criterion for the existence of…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…
Presence of model uncertainties creates challenges for model-based control design, and complexity of the control design is further exacerbated when coping with nonlinear systems. This paper presents a sliding mode control (SMC) design…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…