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Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of…
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
Convolutional neural networks (CNNs) have gained remarkable success in recent years. However, their performance highly relies on the architecture hyperparameters, and finding proper hyperparameters for a deep CNN is a challenging…
Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…
Distributed training of deep neural networks has received significant research interest, and its major approaches include implementations on multiple GPUs and clusters. Parallelization can dramatically improve the efficiency of training…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Optical imaging systems are inherently limited in their resolution due to the point spread function (PSF), which applies a static, yet spatially-varying, convolution to the image. This degradation can be addressed via Convolutional Neural…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical…
We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…
Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale…
A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized…
Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such…
Surrogate-assistance approaches have long been used in computationally expensive domains to improve the data-efficiency of optimization algorithms. Neuroevolution, however, has so far resisted the application of these techniques because it…
With the great success of diffusion models in image generation, diffusion-based image compression is attracting increasing interests. However, due to the random noise introduced in the diffusion learning, they usually produce…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
This study introduces a surrogate modeling framework merging proper orthogonal decomposition, long short-term memory networks, and multi-task learning, to accurately predict elastoplastic deformations in real-time. Superior to single-task…
Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined…