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Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…
A novel method called mixed variable system Monte Carlo tree search (MVSMCTS) formulation is presented for optimization problems considering various types of variables with single and mixed continuous-discrete system. This method utilizes a…
We present the explicit bonding Reaction ensemble Monte Carlo (eb-RxMC) method, designed to sample reversible bonding reactions in macromolecular systems in thermodynamic equilibrium. Our eb-RxMC method is based on the Reaction ensemble…
Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…
The computational cost of traditional first-principles method quickly becomes prohibitively expensive as the number of atoms increases. This challenge is further amplified by the need to evaluate finite-temperature properties with Monte…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
The exact and phaseless variants of Auxiliary-Field Quantum Monte Carlo (AFQMC) have been shown to be capable of producing accurate ground-state energies for a wide variety of systems including those which exhibit substantial electron…
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximations at different levels of accuracy using a hierarchy of…
This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Lo\`eve…
Accurate ab initio calculations of 3d transition metal monoxide molecules have attracted extensive attention because of its relevance in physical and chemical science, as well as theoretical challenges in treating strong electron…
This paper introduces quasi-Monte Carlo latent variable models (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard…
High-order virtual excitations play an important role in microscopic models of nuclear reactions at intermediate energies. However, the factorial growth of their complexity has prevented their consistent inclusion in ab initio many-body…
To facilitate rational molecular and materials design, this research proposes an integrated computational framework that combines stochastic simulation, ab initio quantum chemistry, and molecular docking. The suggested workflow allows…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
Collective variable (CV) or order parameter based enhanced sampling algorithms have achieved great success due to their ability to efficiently explore the rough potential energy landscapes of complex systems. However, the degeneracy of…
Cryo-electron microscopy (cryo-EM) has revolutionized experimental protein structure determination. Despite advances in high resolution reconstruction, a majority of cryo-EM experiments provide either a single state of the studied…
In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PES) with close to first-principles accuracy. Most current MLPs rely on atomic…
The rise of machine learning has greatly influenced the field of computational chemistry, and that of atomistic molecular dynamics simulations in particular. One of its most exciting prospects is the development of accurate,…
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators…