相关论文: Born-Infeld (BI) for AI: Energy-Conserving Descent…

We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…

In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable…

The Energy Conserving Descent (ECD) algorithm was recently proposed (De Luca & Silverstein, 2022) as a global non-convex optimization method. Unlike gradient descent, appropriately configured ECD dynamics escape strict local minima and…

A growing number of applications in particle physics and beyond use neural networks as unbinned likelihood ratio estimators applied to real or simulated data. Precision requirements on the inference tasks demand a high-level of stability…

The Born-Infeld (BI) model is a nonlinear correction of Maxwell's equations. By adding the energy and Poynting vector as additional variables, it can be augmented as a 10$\times$10 system of hyperbolic conservation laws, called the…

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected…

Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…

Inertial Confinement Fusion (ICF) holds transformative promise for sustainable, near-limitless clean energy, yet remains constrained by prohibitively high costs and limited experimental opportunities. This paper presents Human-in-the-Loop…

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…

Bayesian optimization (BO) has gained attention as an efficient algorithm for black-box optimization of expensive-to-evaluate systems, where the BO algorithm iteratively queries the system and suggests new trials based on a probabilistic…

Second-order flows in this paper refer to some artificial evolutionary differential equations involving second-order time derivatives distinguished from gradient flows which are considered to be first-order flows. This is a popular topic…

We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…

In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…

We study the equilibrium dynamics of a weakly interacting Bose-Einstein condensate trapped in a box. In our approach we use a semiclassical approximation similar to the description of a multi-mode laser. In dynamical equations derived from…

Motivated by the success of Bayesian optimisation algorithms in the Euclidean space, we propose a novel approach to construct Intrinsic Bayesian optimisation (In-BO) on manifolds with a primary focus on complex constrained domains or…

Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this…

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems…

Progress of AI has led to very successful, but by no means humble models and tools, especially regarding (i) the huge and further exploding costs and resources they demand, and (ii) the over-confidence of these tools with the answers they…

In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…

It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…