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This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…
Nonequilibrium physics encompasses a broad range of natural and synthetic small-scale systems. Optimizing transitions of such systems will be crucial for the development of nanoscale technologies and may reveal the physical principles…
This thesis is devoted to the study of dynamical properties of diluted models. These are mean field statistical mechanics systems, but with finite local connectivity. Among other reasons, the interest for these models arises from their deep…
A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…
Systems composed of large numbers of interacting agents often admit an effective coarse-grained description in terms of a multidimensional stochastic dynamical system, driven by small-amplitude intrinsic noise. In applications to…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical…
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
Many physical phenomena may be modelled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the mass is conserved during the evolution, but the momentum…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most…
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…