Related papers: A general optimization framework for mapping local…
In this work, we present a transition-state optimization protocol based on the Mode-Tracking algorithm [J. Chem. Phys. 118 (2003) 1634]. By calculating only the eigenvector of interest instead of diagonalizing the full Hessian matrix and…
The recently proposed excitonic renormalization framework presents an alternative ansatz to elec- tronic structure theory of weakly interacting fragments. It makes use of absolutely localized orbitals and correlated states evaluated on…
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
A long-standing and difficult problem in, e.g., condensed matter physics is how to find the ground state of a complex many-body system where the potential energy surface has a large number of local minima. Spin systems containing complex…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
Local optimization of adsorption systems inherently involves different scales: within the substrate, within the molecule, and between molecule and substrate. In this work, we show how the explicit modeling of the different character of the…
We report a new algorithm for constructing pathways between local minima that involve a large number of intervening transition states on the potential energy surface. A significant improvement in efficiency has been achieved by changing the…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
This paper studies system identification for nonlinear state-space models, a problem that arises across many fields yet remains challenging in practice. Focusing on maximum likelihood estimation, we employ Bayesian optimization (BayesOpt)…
This paper introduces OptiGridML, a machine learning framework for discrete topology optimization in power grids. The task involves selecting substation breaker configurations that maximize cross-region power exports, a problem typically…
Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches…
When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area.…
We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…
Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is…
The ubiquitous expansion and transformation of the energy supply system involves large-scale power infrastructure construction projects. In the view of investments of more than a million dollars per kilometre, planning authorities aim to…
Topology optimization is used for the design of high-performance structures but remains fundamentally limited by its iterative nature, requiring repeated finite element analyses that prevent real-time deployment and large-scale design…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient…
This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of…
We develop a geometric convergence theory for neural-network optimization within the minimizing movement scheme (MMS) framework. Reformulating each neural MMS step as a minimization over the set of increments in a Hilbert space, we show…