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We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
The problem of function approximation by neural dynamical systems has typically been approached in a top-down manner: Any continuous function can be approximated to an arbitrary accuracy by a sufficiently complex model with a given…
Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…
Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive…
Edge training of Deep Neural Networks (DNNs) is a desirable goal for continuous learning; however, it is hindered by the enormous computational power required by training. Hardware approximate multipliers have shown their effectiveness for…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
This paper addresses the challenges of embedding common droop control characteristics in ac-dc power system steady-state simulation and optimization problems. We propose a smooth approximation methodology to construct differentiable…
Design considerations for molecular dynamics algorithms capable of taking advantage of the computational power of a graphics processing unit (GPU) are described. Accommodating the constraints of scalable streaming-multiprocessor hardware…
Event-driven molecular dynamics is a valuable tool in condensed and soft matter physics when particles can be modeled as hard objects or more generally if their interaction potential can be modeled in a stepwise fashion. Hard spheres model…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
In this paper we present advanced representation learning study on integrating deep learning techniques and sparse approximation, including diffusion models, for advanced flow field analysis and reconstruction. Key applications include…
Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…
Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…
The article describes the diffusion approximation and the method of its use for evaluation of the effectiveness of active queue management (AQM) mechanisms. The presented model combines the approximation and simulation approaches. The…
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…