Related papers: Dynamical field inference and supersymmetry
We analyze the dynamics of a Dirac-Born-Infeld (DBI) field in a cosmological set-up which includes a perfect fluid. Introducing convenient dynamical variables, we show the evolution equations form an autonomous system when the potential and…
We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…
Understanding how deep learning architectures work is a central scientific problem. Recently, a correspondence between neural networks (NNs) and Euclidean quantum field theories (QFTs) has been proposed. This work investigates this…
An antithetical concept, adaptive symmetry, to conservative symmetry in physics is proposed to understand the deep neural networks (DNNs). It characterizes the invariance of variance, where a biotic system explores different pathways of…
Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation…
With rapid progress in deep learning, neural networks have been widely used in scientific research and engineering applications as surrogate models. Despite the great success of neural networks in fitting complex systems, two major…
Modern machine learning models are typically trained via multi-pass stochastic gradient descent (SGD) with small batch sizes, and understanding their dynamics in high dimensions is of great interest. However, an analytical framework for…
The superadiabatic dynamical density functional theory (superadiabatic-DDFT) is a promising new method for the study of colloidal systems out-of-equilibrium. Within this approach the viscous forces arising from interparticle interactions…
Site density functional theory (SDFT) provides a rigorous framework for statistical mechanics analysis of inhomogeneous molecular liquids. The key defining feature of these systems is the presence of two very distinct interactions scales…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
Building on previous work on the stochastic analysis for Grassmann random variables, we introduce a forward-backward stochastic differential equation (FBSDE) which provides a stochastic quantisation of Grassmann measures. Our method is…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
Axiomatic quantum field theory (QFT) provides a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of…
Efficient sampling from un-normalized target distributions is pivotal in scientific computing and machine learning. While neural samplers have demonstrated potential with a special emphasis on sampling efficiency, existing neural implicit…
Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In…
Although the classical density functional theory (DFT) of inhomogeneous fluids was formulated more than four decades ago, its application to broken symmetry phases of molecular systems remained a challenge. Approximate free energy…
A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these…
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…
The article represents a research of the cosmological evolution of fermion statistical systems with fantom scalar interaction where "kinetic" term's contribution to the total energy of a scalar field is negative. As a result of analytical…