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Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at…
Control of nonlinear uncertain systems is a common challenge in the robotics field. Nonlinear latent force models, which incorporate latent uncertainty characterized as Gaussian processes, carry the promise of representing such systems…
We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Photonic accelerators have recently attracted soaring interest, harnessing the ultimate nature of light for information processing. Collective decision-making with a laser network, employing the chaotic and synchronous dynamics of optically…
Reinforcement learning involves decision making in dynamic and uncertain environments, and constitutes one important element of artificial intelligence (AI). In this paper, we experimentally demonstrate that the ultrafast chaotic…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…
Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…
Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit…
Photonic accelerators have been intensively studied to provide enhanced information processing capability to benefit from the unique attributes of physical processes. Recently, it has been reported that chaotically oscillating ultrafast…
In this paper, we study a linear-quadratic partially observed Stackelberg stochastic differential game problem in which a single leader and multiple followers are involved. We consider more practical formulation for partial information that…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…
It is sometimes difficult to achieve a complete observation for a full set of observables, and partial observations are necessary. For deterministic systems, the Mori-Zwanzig formalism provides a theoretical framework for handling partial…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…
Evaluating the effectiveness and benefits of driver assistance systems is crucial for improving the system performance. In this paper, we propose a novel framework for testing and evaluating lane departure correction systems at a low cost…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
Machine Learning and Deep Learning are computational tools that fall within the domain of artificial intelligence. In recent years, numerous research works have advanced the application of machine and deep learning in various fields,…
The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…