Related papers: Data-driven discovery of polynomial ODEs with prov…
The separation of overlapping objects presents a significant challenge in scientific imaging. While deep learning segmentation-regression algorithms can predict pixel-wise intensities, they typically treat all regions equally rather than…
Mirror descent plays a crucial role in constrained optimization and acceleration schemes, along with its corresponding low-resolution ordinary differential equations (ODEs) framework have been proposed. However, the low-resolution ODEs are…
We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing…
When applying deep learning models in open-world scenarios, active learning (AL) strategies are crucial for identifying label candidates from a nearly infinite amount of unlabeled data. In this context, robust out-of-distribution (OOD)…
The generalized Lasso is a remarkably versatile and extensively utilized model across a broad spectrum of domains, including statistics, machine learning, and image science. Among the optimization techniques employed to address the…
We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which…
This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
This paper introduces a novel approach for learning polynomial representations of physical objects. Given a point cloud data set associated with a physical object, we solve a one-class classification problem to bound the data points by a…
This paper presents an intrinsic approach for addressing control problems with systems governed by linear ordinary differential equations (ODEs). We use computer algebra to constrain a Gaussian Process on solutions of ODEs. We obtain…
Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are extremely sparse, which severely limits the applicability of both…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…
Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
A discrete-time linear dynamical system (LDS) is given by an update matrix $M \in \mathbb{R}^{d\times d}$, and has the trajectories $\langle s, Ms, M^2s, \ldots \rangle$ for $s \in \mathbb{R}^d$. Reachability-type decision problems of…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by…
We tersely review a recently introduced technique to identify systems of two nonlinearly-coupled Ordinary Di{\S}erential Equations (ODEs) solvable by algebraic operations; and we report some specifc examples of this kind, namely systems of…