Related papers: Extending the multi-level method for the simulatio…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
Optimization via simulation has been well established to find optimal solutions and designs in complex systems. However, it still faces modeling and computational challenges when extended to the multi-stage setting. This survey reviews the…
A complex system is made up of many components with many interactions. So the design of systems such as simulation systems, cooperative systems or assistance systems includes a very accurate modelling of interactional and communicational…
Bilevel optimization has been successfully applied to many important machine learning problems. Algorithms for solving bilevel optimization have been studied under various settings. In this paper, we study the nonconvex-strongly-convex…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Estimating a causal query from observational data is an essential task in the analysis of biomolecular networks. Estimation takes as input a network topology, a query estimation method, and observational measurements on the network…
The practical application requests both accuracy and efficiency on multi-person pose estimation algorithms. But the high accuracy and fast inference speed are dominated by top-down methods and bottom-up methods respectively. To make a…
The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…
We consider the problem of numerically estimating expectations of solutions to stochastic differential equations driven by Brownian motions in the commonly occurring small noise regime. We consider (i) standard Monte Carlo methods combined…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different…
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be…
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
A random-batch method for multi-species interacting particle systems is proposed, extending the method of S. Jin, L. Li, and J.-G. Liu [J. Comput. Phys. 400 (2020), 108877]. The idea of the algorithmus is to randomly divide, at each time…
The design of provably correct controllers for continuous-state stochastic systems crucially depends on approximate finite-state abstractions and their accuracy quantification. For this quantification, one generally uses approximate…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Multilevel modeling and simulation (M&S) is becoming increasingly relevant due to the benefits that this methodology offers. Multilevel models allow users to describe a system at multiple levels of detail. From one side, this can make…
A multilevel network is defined as the junction of two interaction networks, one level representing the interactions between individuals and the other the interactions between organizations. The levels are linked by an affiliation…