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Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
An underlying structure in several sampling-based methods for continuous multi-robot motion planning (MRMP) is the tensor roadmap (TR), which emerges from combining multiple PRM graphs constructed for the individual robots via a tensor…
Periodic fin structures are often employed to enhance heat transfer in compact cooling solutions and heat exchangers. Adjoint-based optimization methods are able to further increase the heat transfer by optimizing the fin geometry. However,…
In the classical interval scheduling type of problems, a set of $n$ jobs, characterized by their start and end time, need to be executed by a set of machines, under various constraints. In this paper we study a new variant in which the jobs…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and…
We apply Pontryagin's principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $\kappa$. We work out the optimal time…
Stochastic Gradient Descent is used for large datasets to train models to reduce the training time. On top of that data parallelism is widely used as a method to efficiently train neural networks using multiple worker nodes in parallel.…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
In statistical physics, the efficiency of tempering approaches strongly depends on ingredients such as the number of replicas $R$, reliable determination of weight factors and the set of used temperatures, ${\mathcal T}_R = \{T_1, T_2,…
Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary problems. The reason for this is that time-dependent problems…
Jarzynski's equality sets a strong bound on the probability of violating the second law of thermodynamics by extracting work beyond the free energy difference. We derive finite-time refinements to this bound for driven systems in contact…
Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100%…
Time-periodic driving provides a promising route to engineer non-trivial states in quantum many-body systems. However, while it has been shown that the dynamics of integrable systems can synchronize with the driving into a non-trivial…
Predicting the response of an observed system to a known input is a fruitful first step to accurately control the system's dynamics. Despite the recent advances in fully data-driven algorithms, the most interpretable way to reach this goal…
Designing a protocol to efficiently drive a stochastic system is an active field of research. Here we extend such control theory to an active Ornstein-Uhlenbeck particle (AOUP) in a bistable potential, driven by a harmonic trap. We find…
Stochastic Processing Networks (SPNs) can be used to model communication networks, manufacturing systems, service systems, etc. We consider a real-time SPN where tasks generate jobs with strict deadlines according to their traffic patterns.…
The control of active colloidal particles via optical traps is a cornerstone for research of matter at the micron and nanometer scale. A central challenge in this domain is the derivation of optimal transport protocols that minimize the…