相关论文: Born-Infeld (BI) for AI: Energy-Conserving Descent…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…
An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is…
We propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by…
Stochastic thermodynamics lays down a broad framework to revisit the venerable concepts of heat, work and entropy production for individual stochastic trajectories of mesoscopic systems. Remarkably, this approach, relying on stochastic…
In this study, we present a novel method for enhancing the computational efficiency of whole-body control for humanoid robots, a challenge accentuated by their high degrees of freedom. The reduced-dimension rigid body dynamics of a floating…
Logic optimization constitutes a critical phase within the Electronic Design Automation (EDA) flow, essential for achieving desired circuit power, performance, and area (PPA) targets. These logic circuits are typically represented as…
Fragmented Bose-Einstein condensates are large systems of identical bosons displaying \emph{multiple} macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the…
This study addresses the challenge of fleet design optimization in the context of heterogeneous multi-robot fleets, aiming to obtain feasible designs that balance performance and costs. In the domain of autonomous multi-robot exploration,…
Systems involving Partial Differential Equations (PDEs) have recently become more popular among the machine learning community. However prior methods usually treat infinite dimensional problems in finite dimensions with Reduced Order…
Degenerate Cahn-Hilliard phase-field models provide a robust approximation of surface-diffusion-driven interface motion without explicit front tracking. In computations, however, the geometric volume enclosed by the interface -- the region…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an…
We initiate the study of utilizing Quantum Langevin Dynamics (QLD) to solve optimization problems, particularly those non-convex objective functions that present substantial obstacles for traditional gradient descent algorithms.…
In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size,…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
Optimal experimental design (OED) seeks experiments expected to yield the most useful data for some purpose. In practical circumstances where experiments are time-consuming or resource-intensive, OED can yield enormous savings. We pursue…
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…