Related papers: Data-driven Evolutions of Critical Points
In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…
The widespread deployment of power electronic technologies is transforming modern power systems into fast, nonlinear, and heterogeneous networks. Conventional modeling and control approaches, rooted in quasi-static analysis and centralized…
This work presents a new modeling approach to macroscopic, polycrystalline elasto-plasticity starting from first principles and a few well-defined structural assumptions, incorporating the mildly rate-dependent (viscous) nature of plastic…
Reuse of data in adaptive workflows poses challenges regarding overfitting and the statistical validity of results. Previous work has demonstrated that interacting with data via differentially private algorithms can mitigate overfitting,…
We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models…
Attaining prototypical features to represent class distributions is well established in representation learning. However, learning prototypes online from streaming data proves a challenging endeavor as they rapidly become outdated, caused…
When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…
We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time…
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
In many real-world scenarios, we often deal with streaming data that is sequentially collected over time. Due to the non-stationary nature of the environment, the streaming data distribution may change in unpredictable ways, which is known…
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
We rigorously derive linear elasticity as a low energy limit of pure traction nonlinear elasticity. Unlike previous results, we do not impose any restrictive assumptions on the forces, and obtain a full $\Gamma$-convergence result. The…
When deploying autonomous agents in unstructured environments over sustained periods of time, adaptability and robustness oftentimes outweigh optimality as a primary consideration. In other words, safety and survivability constraints play a…
Transient growth analysis has been extensively studied in asymptotically stable flows to identify their short-term amplification of perturbations. Generally, in global transient growth analyses, matrix-free methods are adopted, requiring…
We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical…
This paper presents an approach for data-driven policy refinement in reinforcement learning, specifically designed for safety-critical applications. Our methodology leverages the strengths of data-driven optimization and reinforcement…