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A global hybrid extension of variational two-electron reduced-density matrix (v2RDM)-driven multiconfiguration pair-density functional theory (MCPDFT) is developed. Using a linear decomposition of the electron-electron repulsion term, a…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Markov Decision Processes are classically solved using Value Iteration and Policy Iteration algorithms. Recent interest in Reinforcement Learning has motivated the study of methods inspired by optimization, such as gradient ascent. Among…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
The constrained Markov decision process (CMDP) framework emerges as an important reinforcement learning approach for imposing safety or other critical objectives while maximizing cumulative reward. However, the current understanding of how…
The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many body Schr\"{o}dinger equation. The…
We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our…
Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
We propose an exact algorithm for computing the analytical gradient within the framework of the orbital-specific-virtual (OSV) second-order M{\o}ller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the exact…
Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without…
Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings as well as the inherently multiconfigurational character of excited states. As such, one needs a multi-state…
We develop analytical gradients of ground- and excited-state energies with respect to system parameters including the nuclear coordinates for the hybrid quantum/classical multistate contracted variational quantum eigensolver (MC-VQE)…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…
Policy gradient algorithms have been widely applied to Markov decision processes and reinforcement learning problems in recent years. Regularization with various entropy functions is often used to encourage exploration and improve…
The multiscale model combining the multiconfigurational self-consistent field (MCSCF) method with the fully atomistic polarizable Fluctuating Charges (FQ) force field (J. Chem. Theory Comput. 2024, 20, 9954-9967) is here extended to the…
We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a…
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…