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A topological neural network (TNN), which takes data from a Tychonoff topological space instead of the usual finite dimensional space, is introduced. As a consequence, a distributional neural network (DNN) that takes Borel measures as data…

This review deals with Restricted Boltzmann Machine (RBM) under the light of statistical physics. The RBM is a classical family of Machine learning (ML) models which played a central role in the development of deep learning. Viewing it as a…

Neural networks are nowadays both powerful operational tools (e.g., for pattern recognition, data mining, error correction codes) and complex theoretical models on the focus of scientific investigation. As for the research branch, neural…

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify…

We introduce the \emph{Symplectic Generative Network (SGN)}, a deep generative model that leverages Hamiltonian mechanics to construct an invertible, volume-preserving mapping between a latent space and the data space. By endowing the…

Symmetry is omnipresent in nature and perceived by the visual system of many species, as it facilitates detecting ecologically important classes of objects in our environment. Symmetry perception requires abstraction of long-range spatial…

Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a…

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…

Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…

Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Deep Boltzmann Machines (DBMs) are generative neural networks with these desired properties. We integrate a DBM…

Deep belief networks (DBNs) are stochastic neural networks that can extract rich internal representations of the environment from the sensory data. DBNs had a catalytic effect in triggering the deep learning revolution, demonstrating for…

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…

Dynamic network models (DNMs) are belief networks for temporal reasoning. The DNM methodology combines techniques from time series analysis and probabilistic reasoning to provide (1) a knowledge representation that integrates…

In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key…

interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted…

Despite the practical success of deep neural networks, a comprehensive theoretical framework that can predict practically relevant scores, such as the test accuracy, from knowledge of the training data is currently lacking. Huge…

The development of modern ab initio methods has rapidly increased our understanding of physics, chemistry and materials science. Unfortunately, intensive ab initio calculations are intractable for large and complex systems. On the other…

The pioneer deep neural networks (DNNs) have emerged to be deeper or wider for improving their accuracy in various applications of artificial intelligence. However, DNNs are often too heavy to deploy in practice, and it is often required to…