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The majority of the research on the quantization of Deep Neural Networks (DNNs) is focused on reducing the precision of tensors visible by high-level frameworks (e.g., weights, activations, and gradients). However, current hardware still…
Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…
The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, Deep Learning, and especially Convolutional Neural Networks (CNN), has been introduced to solve this…
The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the…
We present a deep learning framework for correcting existing dynamical system models utilizing only a scarce high-fidelity data set. In many practical situations, one has a low-fidelity model that can capture the dynamics reasonably well…
Data I/O poses a significant bottleneck in large-scale CFD simulations; thus, practitioners would like to significantly reduce the number of times the solution is saved to disk, yet retain the ability to recover any field quantity (at any…
Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with…
Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSN), but current simulations must rely on subgrid models since direct numerical simulation (DNS) is too expensive. Unfortunately, existing…
We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…
This paper tackles the problem of training a deep convolutional neural network with both low-precision weights and low-bitwidth activations. Optimizing a low-precision network is very challenging since the training process can easily get…
Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…
In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…
Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations…
The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…
Scientific computing has long relied on double precision (64-bit floating point) arithmetic to guarantee accuracy in simulations of real-world phenomena. However, the growing availability of hardware accelerators such as Graphics Processing…
Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior. The…
Uncertainty is a fundamental aspect of real-world scenarios, where perfect information is rarely available. Humans naturally develop complex internal models to navigate incomplete data and effectively respond to unforeseen or partially…
Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively…
The simulation of partial differential equations is a central subject of numerical analysis and an indispensable tool in science, engineering and related fields. Existing approaches, such as finite elements, provide (highly) efficient tools…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…