Related papers: HMC and gradient flow with machine-learned classic…
For addressing optimisation tasks on finite dimensional quantum systems, we give a comprehensive account of the foundations of gradient flows on Riemannian manifolds including new developments: we extend former results from Lie groups such…
State-of-the-art simulations of discrete gauge theories are based on Markov chains with local changes in the field space, which however at very fine lattice spacings are notoriously difficult due to separated topological sectors of the…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use…
Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time- and length-scales inaccessible to all-atom simulations. Parameterizing CG force fields to match all-atom simulations has mainly…
In the gradient flow method of lattice gauge theory, coarse graining is performed so as to reduce the action, and as the coarse graining progresses, the field strength becomes very small. However, the confinement property that particles…
We study the optimization of wide neural networks (NNs) via gradient flow (GF) in setups that allow feature learning while admitting non-asymptotic global convergence guarantees. First, for wide shallow NNs under the mean-field scaling and…
While methods exist for aligning flow matching models--a popular and effective class of generative models--with human preferences, existing approaches fail to achieve both adaptation efficiency and probabilistically sound prior…
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…
We propose a renormalisation group inspired normalising flow that combines benefits from traditional Markov chain Monte Carlo methods and standard normalising flows to sample lattice field theories. Specifically, we use samples from a…
This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…
Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural…
We apply the method of Hasenfratz and Niedermayer to analytically construct perfect lattice actions for the Gross--Neveu model. In the large $N$ limit these actions display an exactly perfect scaling, i.e. cut-off artifacts are completely…
In industrial manufacturing processes, errors frequently occur at unpredictable times and in unknown manifestations. We tackle the problem of automatic defect detection without requiring any image samples of defective parts. Recent works…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…
The classically perfect Fixed-Point fermion action for lattice QCD, a highly improved discretization of the continuum theory that preserves chiral symmetry, is constructed in this thesis and a parallel work by T. Jorg. In the framework of…
We investigate the stability of topological charge under gradient flow taking the admissibility condition into account. For the $SU(2)$ Wilson gauge theory with $\beta=2.45$ and $L^4=12^4$, we numerically show that the gradient flows with…
Mathematical Programs with Vanishing Constraints (MPVCs) are a notoriously challenging class of problems owing to their lack of constraint qualification. Therefore, to tackle these problems, relaxation-based approaches are typically used.…
It has been pointed out in recent papers that the example considered earlier in the O(N) sigma-model to test whether fixed-point actions are 1-loop perfect actually checked classical perfection only. To clarify the issue we constructed the…
We present preliminary result for the step-scaling study of the coupling constant with the Yang-Mills gradient flow, in the twelve-favour SU(3) gauge theory. In this work, the lattice simulation is performed using unimproved staggered…