Related papers: Data-Driven Approximate Abstraction for Black-Box …
Modern data-driven control applications call for flexible nonlinear models that are amenable to principled controller synthesis and realtime feedback. Many nonlinear dynamical systems of interest are control affine. We propose two novel…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
In this paper, we investigate discrete-time decision-making problems in uncertain systems with partially observed states. We consider a non-stochastic model, where uncontrolled disturbances acting on the system take values in bounded sets…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Automatic data abstraction is an important capability for both benchmarking machine intelligence and supporting summarization applications. In the former one asks whether a machine can `understand' enough about the meaning of input data to…
Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models…
This paper presents a compositional approach to specification-guided abstraction refinement for control synthesis of a nonlinear system associated with a method to over-approximate its reachable sets. Given an initial coarse partition of…
Learning abstractions directly from data is a core challenge in robotics. Humans naturally operate at an abstract level, reasoning over high-level subgoals while delegating execution to low-level motor skills -- an ability that enables…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
The paper presents a data-driven predictive control framework based on an implicit input-output mapping derived directly from the signal matrix of collected data. This signal matrix model is derived by maximum likelihood estimation with…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Dynamic algorithms come in three main flavors: $\mathit{incremental}$ (insertions-only), $\mathit{decremental}$ (deletions-only), or $\mathit{fully}$ $\mathit{dynamic}$ (both insertions and deletions). Fully dynamic is the holy grail of…
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…
We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable…
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…