Related papers: Simulating first-order phase transition with hiera…

The atomistic modeling of amorphous materials requires structure sizes and sampling statistics that are challenging to achieve with first-principles methods. Here, we propose a methodology to speed up the sampling of amorphous and…

Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers…

In this paper, a new method for solving the power flow problem in distribution systems which is fast, parallel, as well as modular, straightforward, simplified and generic is proposed. This approach is based on a hierarchical construction…

Learning systems must balance generalization across experiences with discrimination of task-relevant details. Effective learning therefore requires representations that support both. Online latent-cause models support incremental inference…

Over the past decade, deep neural networks have proven to be adept in image classification tasks, often surpassing humans in terms of accuracy. However, standard neural networks often fail to understand the concept of hierarchical…

To operate process engineering systems in a safe and reliable manner, predictive models are often used in decision making. In many cases, these are mechanistic first principles models which aim to accurately describe the process. In…

We propose a hierarchical training algorithm for standard feed-forward neural networks that adaptively extends the network architecture as soon as the optimization reaches a stationary point. By solving small (low-dimensional) optimization…

In previous work, it has been shown that the recently proposed LLR method is very efficient at overcoming strong metastabilities that arise near first-order phase transition points. Here we present a systematic study of the performance of…

Machine learning models have become indispensable tools in applications across the physical sciences. Their training is often time-consuming, vastly exceeding the inference timescales. Several protocols have been developed to perturb the…

Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper,…

Determining phase diagrams and phase transitions semi-automatically using machine learning has received a lot of attention recently, with results in good agreement with more conventional approaches in most cases. When it comes to more…

A physics-informed convolutional neural network is proposed to simulate two phase flow in porous media with time-varying well controls. While most of PICNNs in existing literatures worked on parameter-to-state mapping, our proposed network…

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high…

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…

Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data…

Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…

Humans can make predictions on various time scales and hierarchical levels. Thereby, the learning of event encodings seems to play a crucial role. In this work we model the development of hierarchical predictions via autonomously learned…

Multivariate time series forecasting with hierarchical structure is widely used in real-world applications, e.g., sales predictions for the geographical hierarchy formed by cities, states, and countries. The hierarchical time series (HTS)…

We introduce a new approach to hierarchy formation and task decomposition in hierarchical reinforcement learning. Our method is based on the Hierarchy Of Abstract Machines (HAM) framework because HAM approach is able to design efficient…