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The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns…
We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators…
We propose a general framework for parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in…
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) in distribution systems by solving the so-called optimal power flow (OPF) problem. The OPF problem is concerned…
In this paper, a distributed optimal steady-state regulation problem is formulated and investigated for heterogeneous linear multi-agent systems subject to external disturbances. We aim to steer this high-order multi-agent network to a…
We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over…
This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic…
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…
The calibration of simulators for complex social systems aims to identify the optimal parameter that drives the output of the simulator best matching the target data observed from the system. As many social systems may change internally…
Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of…
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the…
Two-stage risk-averse distributionally robust optimization (DRO) problems are ubiquitous across many engineering and business applications. Despite their promising resilience, two-stage DRO problems are generally computationally…
Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system…
Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to…
We investigate the creation of entangled states of bright light beams obeying the condition of strong Einstein-Podolsky-Rosen-like paradox criterion in time-modulated quantum dissipative dynamics. Having in view the generation of these…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
Several types of biological networks have recently been shown to be accurately described by a maximum entropy model with pairwise interactions, also known as the Ising model. Here we present an approach for finding the optimal mappings…