Related papers: Physics-informed renormalisation group flows
The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics…
Array-like collection data structures are widely established in Python's scientific computing-ecosystem for high-performance computations. The structure maps well to regular, gridded lattice structures that are common to computational…
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models.…
We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-$\frac{1}{2}$ systems. Our formalism is suitable for systems with $\textrm{U}(1)$…
High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…
We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress…
We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…
Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…
We formulate a real-space renormalization group (RG) approach for efficient numerical analysis of the low-temperature hopping dynamics in energy-disordered lattices. The approach explicitly relies on the time-scale separation of the…
The phenomenological renormalization group (PRG) has been applied to the study of scaleinvariant phenomena in neuronal data, providing evidence for critical phenomena in the brain. However, it remains unclear how reliably these observed…
Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of domains, including physical, engineered,…
We systematically study a numerical procedure that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs). This procedure, based on the renormalization group (RG) theory for PDEs, appeared…
The Schwinger-Keldysh functional renormalization group (fRG) developed in [1] is employed to investigate critical dynamics related to a second-order phase transition. The effective action of model A is expanded to the order of…
Developing engineering systems that rely on flow-induced reconfiguration, the phenomenon where a structure deforms under flow to reduce its drag, requires design tools that can predict the behavior of these flexible structures. Current…
We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S = \int d^dx \sqrt{g} f(R)$. Based on this equation we show that certain…
We analyze the Ising model on a random surface with a boundary magnetic field using matrix model techniques. We are able to exactly calculate the disk amplitude, boundary magnetization and bulk magnetization in the presence of a boundary…
We present a unified framework for the renormalisation of the Hamiltonian and eigenbasis of a system of correlated electrons, unveiling thereby the interplay between electronic correlations and many-particle entanglement. For this, we…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…