Related papers: Data-driven, structure-preserving approximations t…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
Forecasting traffic flows is a central task in intelligent transportation system management. Graph structures have shown promise as a modeling framework, with recent advances in spatio-temporal modeling via graph convolution neural…
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based on Abernethy and Hazan's sketch of a universal interior…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
We use guiding principles from nonequilibrium thermodynamics to develop an admissible set of 13 moment equations for rarefied gas flows. The main benefits of our thermodynamic approach are an explicit entropy expression fulfilling an $H$…
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not…
We investigate the impact of momentum-dependent relaxation time approximation in the Boltzmann equation within the Bjorken flow framework by analyzing the moments of the single-particle distribution function. The moment equations, which…
Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of…
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and…
We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
Data-based safe gain-scheduling controllers are presented for discrete-time linear parameter-varying systems (LPV) with polytopic models. First, $\lambda$-contractivity conditions are provided under which safety and stability of the LPV…
The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of…
Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…
We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis.…
Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has…