Related papers: Deterministic and stochastic surrogate models for …
Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty…
The treatment of Hall-effect thrusters as nonlinear, dynamical systems has emerged as a new perspective to understand and analyze data acquired from the thrusters. The acquisition of high-speed data that can resolve the characteristic…
In this paper, we consider the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. For this class of systems, the superposition principle allows us to…
Accurate and predictive scale-resolving simulations of laser-ignited rocket engines are highly time-consuming because the problem includes turbulent fuel-oxidizer mixing dynamics, laser-induced energy deposition, and high-speed flame…
Fast surrogate models for expensive simulations are now essential across the sciences, yet they typically operate as black boxes. We present \texttt{GWAgent}, a large language model (LLM)-based workflow that constructs interpretable…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
We apply perturbative techniques to a driven undamped sinusoidal oscillator at resonance. The angular displacement, $\theta$, obeys the dynamics $\Ddot{\theta} + \omega^{2} \sin{\theta} = H\cos{\omega t}$. The linearized approximation gives…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving…
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work…
Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude…
Computer simulations, especially of complex phenomena, can be expensive, requiring high-performance computing resources. Often, to understand a phenomenon, multiple simulations are run, each with a different set of simulation input…
Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…
Surrogate models are effective tools for accelerated design of complex systems. The result of a design optimization procedure using surrogate models can be used to initialize an optimization routine using the full order system. High…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…
We propose an extension of the Ewens measure on permutations by choosing the cycle weights to be asymptotically proportional to the degree of the symmetric group. This model is primarily motivated by a natural approximation to the so-called…
Surrogate modeling and active subspaces have emerged as powerful paradigms in computational science and engineering. Porting such techniques to computational models in the social sciences brings into sharp relief their limitations in…