Related papers: Compression challenges in large scale PDE solvers
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for…
This work is concerned with the quantification of the epistemic uncertainties induced the discretization of partial differential equations. Following the paradigm of probabilistic numerics, we quantify this uncertainty probabilistically.…
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…
Differential privacy (DP) has become the de facto standard of privacy preservation due to its strong protection and sound mathematical foundation, which is widely adopted in different applications such as big data analysis, graph data…
Freight carriers rely on tactical plans to satisfy demand in a cost-effective way. For computational tractability in real large-scale settings, such plans are typically computed by solving deterministic and cyclic formulations. An important…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
Bringing a high-dimensional dataset into science-ready shape is a formidable challenge that often necessitates data compression. Compression has accordingly become a key consideration for contemporary cosmology, affecting public data…
Machine learning at the edge offers great benefits such as increased privacy and security, low latency, and more autonomy. However, a major challenge is that many devices, in particular edge devices, have very limited memory, weak…
Partial Differential Equations are precise in modelling the physical, biological and graphical phenomena. However, the numerical methods suffer from the curse of dimensionality, high computation costs and domain-specific discretization. We…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through…
Coupled 3D-1D problems arise in many practical applications, in an attempt to reduce the computational burden in simulations where cylindrical inclusions with a small section are embedded in a much larger domain. Nonetheless the resolution…
Communicating information, like gradient vectors, between computing nodes in distributed and federated learning is typically an unavoidable burden, resulting in scalability issues. Indeed, communication might be slow and costly. Recent…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…
Iterative methods on irregular grids have been used widely in all areas of comptational science and engineering for solving partial differential equations with complex geometry. They provide the flexibility to express complex shapes with…