Related papers: A fast time-stepping strategy for dynamical system…
Linearly implicit Runge-Kutta methods with approximate matrix factorization can solve efficiently large systems of differential equations that have a stiff linear part, e.g. reaction-diffusion systems. However, the use of approximate…
Recent years have seen a surge in deep learning approaches to accelerate numerical solvers, which provide faithful but computationally intensive simulations of the physical world. These deep surrogates are generally trained in a supervised…
We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical…
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge--Kutta method. The…
This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…
We propose a novel functional approach to surrogate modeling of dynamical systems with exogenous inputs. This approach, named Functional Nonlinear AutoRegressive with eXogenous inputs (F-NARX), approximates the system response based on…
This article extends the theory of dual-consistent summation-by-parts (SBP) and generalized SBP (GSBP) time-marching methods by showing that they are implicit Runge-Kutta schemes. Through this connection, the accuracy theory for the…
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…
Performing reliability analysis on complex systems is often computationally expensive. In particular, when dealing with systems having high input dimensionality, reliability estimation becomes a daunting task. A popular approach to overcome…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
We present a novel machine learning-based approach to generate fast-executing virtual radiofrequency quadrupole (RFQ) particle accelerators using surrogate modelling. These could potentially be used as on-line feedback tools during beam…
Accurately modeling the spatio-temporal dynamics of blast wave propagation remains a longstanding challenge due to its highly nonlinear behavior, sharp gradients, and burdensome computational cost. While machine learning-based surrogate…
Recent advancements in QA with LLM, like GPT-4, have shown limitations in handling complex multi-hop queries. We propose AT-RAG, a novel multistep RAG incorporating topic modeling for efficient document retrieval and reasoning. Using…
Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…
Most real-world optimization problems are difficult to solve with traditional statistical techniques or with metaheuristics. The main difficulty is related to the existence of a considerable number of local optima, which may result in the…
Simulations of optical quantum systems are essential for the development of quantum technologies. However, these simulations are often computationally intensive, especially when repeated evaluations are required for data fitting, parameter…
Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…
Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…
Computational Fluid Dynamics (CFD) is central to race-car aerodynamic development, yet its cost -- tens of thousands of core-hours per high-fidelity evaluation -- severely limits the design space exploration feasible within realistic…
Temporal surrogate models are effective for predicting chaotic dynamical systems where computational cost can be prohibitive. Several deep neural network architectures can be used for such purposes. In this work, a few commonly used…