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Addressing real-world optimization challenges requires not only advanced metaheuristics but also continuous refinement of their internal mechanisms. This paper explores the integration of machine learning in the form of neural surrogate…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
We consider the problem of learning stabilizable systems governed by nonlinear state equation $h_{t+1}=\phi(h_t,u_t;\theta)+w_t$. Here $\theta$ is the unknown system dynamics, $h_t $ is the state, $u_t$ is the input and $w_t$ is the…
Biophysical neural system simulations are among the most computationally demanding scientific applications, and their optimization requires navigating high-dimensional parameter spaces under numerous constraints that impose a binary…
Model-based controllers learned from data have the biases and noise of their training trajectories, making it important to know which trajectories help or hurt closed-loop performance. Influence functions, widely used in machine learning…
In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on…
Mechanically induced crystallographic phase transformation that reflects dynamic stress responses of intrinsically stochastic nature is a pertinent yet much less well-understood phenomenon. We focus on understanding the physical…
Stochastic simulators are non-deterministic computer models which provide a different response each time they are run, even when the input parameters are held at fixed values. They arise when additional sources of uncertainty are affecting…
Neural surrogates enable orders-of-magnitude acceleration of computational fluid dynamics (CFD) simulations, with the potential to transform engineering and healthcare workflows. Neural surrogate use in real-world applications requires…
Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma…
A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a…
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…
Surrogate modeling is a viable solution for applications involving repetitive evaluations of expensive computational fluid dynamics models, such as uncertainty quantification and inverse problems. This study proposes a multi-layer…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…
Designing materials with controlled heat flow at the nano-scale is central to advances in microelectronics, thermoelectrics, and energy-conversion technologies. At these scales, phonon transport follows the Boltzmann Transport Equation…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
A Cahn-Hilliard equation with stochastic multiplicative noise and a random convection term is considered. The model describes isothermal phase-separation occurring in a moving fluid, and accounts for the randomness appearing at the…