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This paper presents an optimal dynamic control framework for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations affected by both state and process noise. Rather than directly stabilizing the uncertain system,…
Autoregressive neural simulators now match classical solvers on short-horizon prediction of physical systems, yet their accuracy degrades rapidly when rolled out over long horizons. In this work, we identify transient amplification of…
Deformable continuum robots (DCRs) present unique planning challenges due to nonlinear deformation mechanics and partial state observability, violating the Markov assumptions of conventional reinforcement learning (RL) methods. While…
Hybrid models and Neural Differential Equations (NDE) are getting increasingly important for the modeling of physical systems, however they often encounter stability and accuracy issues during long-term integration. Training on unrolled…
The complexities in the dynamic model of the legged robots make it necessary to utilize model-free controllers in the task of trajectory tracking. In This paper, an adaptive transpose Jacobian approach is proposed to deal with the dynamic…
We introduce a weak notion of $2\times 2$-minors of gradients of a suitable subclass of $BV$ functions. In the case of maps in $BV(\mathbb{R}^2;\mathbb{R}^2)$ such a notion extends the standard definition of Jacobian determinant to…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
This work introduces the concept of tangent space regularization for neural-network models of dynamical systems. The tangent space to the dynamics function of many physical systems of interest in control applications exhibits useful…
In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the…
Dynamic polarization control (DPC) is beneficial for many optical applications. It uses adjustable waveplates to perform automatic polarization tracking and manipulation. Efficient algorithms are essential to realizing an endless…
Tendon-Driven Continuum Robots (TDCRs) pose significant control challenges due to their highly nonlinear, path-dependent dynamics and non-Markovian characteristics. Traditional Jacobian-based controllers often struggle with…
We investigate whether Jacobi preconditioning, accounting for the bootstrap term in temporal difference (TD) learning, can help boost performance of adaptive optimizers. Our method, TDprop, computes a per parameter learning rate based on…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
Transport of point-size Brownian particles under the influence of a constant and uniform force field through a three-dimensional channel with smoothly varying periodic cross-section is investigated. Here, we employ an asymptotic analysis in…
Real-time recurrent learning (RTRL) computes exact online gradients by propagating a Jacobian tensor forward through recurrent dynamics, but at O(n^4) cost per step. Prior work has sought structured approximations (rank-1 compression,…
Modern machine learning models struggle to maintain performance in dynamic environments where temporal distribution shifts, \emph{i.e., concept drift}, are prevalent. Temporal Domain Generalization (TDG) seeks to enable model generalization…
Uncertainty in estimation of Drake Passage transport is analyzed in a Hessian-based uncertainty quantification (UQ) framework. The approach extends the adjoint-based ocean state estimation method to provide formal error bounds…
Domain transfer (DT) maps source to target distributions and supports tasks such as unsupervised image-to-image translation, single-cell analysis, and cross-platform medical imaging. However, DT is fundamentally ill-posed: push-forward…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Biological function arises through the dynamical interactions of multiple subsystems, including those between brain areas, within gene regulatory networks, and more. A common approach to understanding these systems is to model the dynamics…