Related papers: Symplectic Inductive Bias for Data-Driven Target R…

Model-reference adaptive systems refer to a consortium of techniques that guide plants to track desired reference trajectories. Approaches based on theories like Lyapunov, sliding surfaces, and backstepping are typically employed to advise…

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…

An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems…

In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…

We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of…

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…

We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…

This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…

Many real-world networks exhibit hierarchical, tree-like structure and heavy-tailed degree distributions, phenomena not readily captured by standard statistical models for network data. Extensions of the popular continuous latent space…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…

Predicting the mean-field Hamiltonian matrix in density functional theory is a fundamental formulation to leverage machine learning for solving molecular science problems. Yet, its applicability is limited by insufficient labeled data for…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven…

Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…

Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…

The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the…