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We propose a robust numerical framework for PDE-constrained shape optimization and Willmore-driven surface hole filling. To address two central challenges -- slow progress in flat energy landscapes, which can trigger premature stagnation at…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…
We present an extension of our one-body M{\o}ller-Plesset second-order perturbation (OBMP2) method for open-shell systems. We derived the OBMP2 Hamiltonian through the canonical transformation followed by the cumulant approximation to…
We introduce a reusable geometry-optimization engine in PyBEST for analytic, gradient-driven molecular structure optimization, with particular emphasis on orbital-optimized pair coupled-cluster doubles (OOpCCD/AP1roG). The engine interfaces…
This work presents a multi-layered methodology for efficiently accelerating multimodal foundation models (MFMs). It combines hardware and software co-design of transformer blocks with an optimization pipeline that reduces computational and…
We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is…
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…
We develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment…
The past few years have seen considerable progress in algorithmic development for the generation of gauge fields including the effects of dynamical fermions. The Rational Hybrid Monte Carlo (RHMC) algorithm, where Hybrid Monte Carlo is…
We develop an efficient $hp$-finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular arcs. The operators derived from this basis are banded and…
Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization. However, its practical efficiency is limited by the…
The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
In this paper, we tackle channel estimation in millimeter-wave hybrid multiple-input multiple-output systems by considering off-grid effects. In particular, we assume that spatial parameters can take any value in the angular domain, and…
In a recent work, we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational…
In this paper, phase combinations among martensitic variants in shape memory alloys patches and bars are simulated by a hybrid optimization methodology. The mathematical model is based on the Landau theory of phase transformations. Each…
We present an efficient algorithm for computing the exact exchange contributions in the Hartree-Fock and hybrid density functional theory models on the basis of the fast multipole method (FMM). Our algorithm is based on the observation that…
Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear…
In this work, we propose and analyze optimization strategies for the VQE algorithm that combine various methods, including molecular point group symmetries (symmetry adaptation), compact excitation circuits (qubit-excitation-based),…