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This paper modifies a n-dimensional Hopf-Cole transformation to the n-dimensional Burgers' system. We obtain the n-dimensional heat conduction equation through the modification of the Hopf-Cole transformation. Then the fourth-order precise…
We present several finite-temperature recursive Fermi-operator expansion schemes based on the second-order spectral projection (SP2) method. Our approach builds on a previous observation that the electronic structure problem, as formulated…
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…
In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…
Out-of-distribution (OOD) detection is essential to handle the distribution shifts between training and test scenarios. For a new in-distribution (ID) dataset, existing methods require retraining to capture the dataset-specific feature…
Understanding the thermal behavior of additive manufacturing (AM) processes is crucial for enhancing the quality control and enabling customized process design. Most purely physics-based computational models suffer from intensive…
Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear…
Global optimization heuristics are popular to optimize hard non-convex problems. Despite their irrefutably large cost-to-solution, in the lack of other working greedy or convex approaches, global optimization algorithms remain the…
The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…
This work introduces an ensemble parameter estimation framework that enables the Lumped Parameter Linear Superposition (LPLSP) method to generate reduced order thermal models from a single transient dataset. Unlike earlier implementations…
The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model for simulating wind-driven, stratified ocean flows. However, their numerical simulation remains computationally expensive due to the need for high-resolution…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
Temperature monitoring during the life time of heat source components in engineering systems becomes essential to guarantee the normal work and the working life of these components. However, prior methods, which mainly use the interpolate…
The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in…
In this paper, we present CT-AGD (Curvature-Tuned Accelerated Gradient Descent), an optimization method for non-convex optimization problems in deep learning training tasks. CT-AGD is a general boosting procedure that accelerates…
By optimizing the rate-distortion-realism trade-off, generative image compression approaches produce detailed, realistic images instead of the only sharp-looking reconstructions produced by rate-distortion-optimized models. In this paper,…
A deep-learning-based closure model to address energy loss in low-dimensional surrogate models based on proper-orthogonal-decomposition (POD) modes is introduced. Using a transformer-encoder block with easy-attention mechanism, the model…
In this work the development of a machine learning-based Reduced Order Model (ROM) for the investigation of hemodynamics in a patient-specific configuration of Coronary Artery Bypass Graft (CABG) is proposed. The computational domain is…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…