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Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…
Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
Flow matching-based generative models have been integrated into the plug-and-play image restoration framework, and the resulting plug-and-play flow matching (PnP-Flow) model has achieved some remarkable empirical success for image…
Stochastic HYPE is a novel process algebra that models stochastic, instantaneous and continuous behaviour. It develops the flow-based approach of the hybrid process algebra HYPE by replacing non-urgent events with events with…
Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the…
Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights. Building on this perspective, we develop a thermodynamic framework to describe the…
Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
In this paper we present a new method for deriving It\^{o} stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME,…
The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient…
Stochastic video prediction models take in a sequence of image frames, and generate a sequence of consecutive future image frames. These models typically generate future frames in an autoregressive fashion, which is slow and requires the…
We study the dynamics of supervised on-line learning of realizable tasks in feed-forward neural networks. We focus on the regime where the number of examples used for training is proportional to the number of input channels N. Using…
Elucidating reaction mechanisms hinges on efficiently generating transition states (TSs), products, and complete reaction networks. Recent generative models, such as diffusion models for TS sampling and sequence-based architectures for…
Traffic flow forecasting is a fundamental research issue for transportation planning and management, which serves as a canonical and typical example of spatial-temporal predictions. In recent years, Graph Neural Networks (GNNs) and…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…