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When a system is driven out of equilibrium by a time-dependent protocol that modifies the Hamiltonian, it follows a nonequilibrium path. Samples of these paths can be used in nonequilibrium work theorems to estimate equilibrium quantities,…
Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
Estimating free energy differences, an important problem in computational drug discovery and in a wide range of other application areas, commonly involves a computationally intensive process of sampling a family of high-dimensional…
The Bethe-Salpeter Equation (BSE) is the workhorse method to study excitons in materials. The BSE Hamiltonian size, which depends on how many valence-to-conduction band transitions are considered, needs to be chosen to be sufficiently large…
We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
Two-phase sampling is a simple and cost-effective estimation strategy in survey sampling and is widely used in practice. Because the phase-2 sampling probability typically depends on low-cost variables collected at phase 1, naive estimation…
The binomial acceptance correction procedure is studied for particle number distributions detected in high energy reactions in finite regions of the momentum space. We present acceptance correction formulas for scaled variance, skewness,…
Host-guest binding plays a crucial role in the functionality of various systems, and its efficiency is often quantified using the binding free energy, which represents the free-energy difference between the bound and dissociated states.…
This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…
We present a new method to evaluate vibrational free energies of atomic systems without a priori specification of an interatomic potential. Our model-agnostic approach leverages descriptors, high-dimensional feature vectors of atomic…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
Free energy profile (FE Profile) is an essential quantity for the estimation of reaction rate and the validation of reaction mechanism. For chemical reactions in condensed phase or enzymatic reactions, the computation of FE profile at ab…
Obtaining the free energies of condensed phase chemical reactions remains computationally prohibitive for high-level quantum mechanical methods. We introduce a hierarchical machine learning framework that bridges this gap by distilling…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Sampling and Variational Inference (VI) are two large families of methods for approximate inference that have complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI…
Monte Carlo switching moves ("perturbations") are defined between two or more classical Hamiltonians sharing a common ground-state energy. The ratio of the density of states (DOS) of one system to that of another is related to the ensemble…
Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wavefunction of metastable electronic states square-integrable. This makes the electronic structure problem of electronic resonances…