Related papers: Path optimization method for the sign problem caus…
While the sign problem of the Dirac fermion is conditioned by the semi-positivity of a determinant, that of the Majorana fermion is conditioned by the semi-positivity of a Pfaffian. We introduce one sufficient condition for the…
Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash},…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…
We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is…
The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically…
The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from exogenous features before solving. This setting is common to many real-world decision processes, and recently it…
Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a…
Monte Carlo simulations away from half-filling suffer from a sign problem that can be reduced by deforming the contour of integration. Such a transformation, which induces a Jacobian determinant in the Boltzmann weight, can be implemented…
Domain knowledge is useful to improve the generalization performance of learning machines. Sign constraints are a handy representation to combine domain knowledge with learning machine. In this paper, we consider constraining the signs of…
The fermion sign problem remains the primary obstacle in simulating the thermodynamic properties of various fermionic systems. In this work, we present a sign-blocking method to mitigate the numerical instability inherent in the sign…
Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the…
An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost…
Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than…
The fermion bag approach is a new method to tackle fermion sign problems in lattice field theories. Using this approach it is possible to solve a class of sign problems that seem unsolvable by traditional methods. The new solutions emerge…
Monte Carlo calculations in the framework of lattice field theory provide non-perturbative access to the equilibrium physics of quantum fields. When applied to certain fermionic systems, or to the calculation of out-of-equilibrium physics,…
An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…