Related papers: Adaptive Mesh-Quantization for Neural PDE Solvers

Today, large language models have demonstrated their strengths in various tasks ranging from reasoning, code generation, and complex problem solving. However, this advancement comes with a high computational cost and memory requirements,…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Human mesh recovery from single images remains challenging due to inherent depth ambiguity and limited generalization across domains. While recent methods combine regression and optimization approaches, they struggle with poor…

We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…

Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…

Although image super-resolution (SR) problem has experienced unprecedented restoration accuracy with deep neural networks, it has yet limited versatile applications due to the substantial computational costs. Since different input images…

As machine learning inferences increasingly move to edge devices, adapting to diverse computational capabilities, hardware, and memory constraints becomes more critical. Instead of relying on a pre-trained model fixed for all future…

We investigate the compression of deep neural networks by quantizing their weights and activations into multiple binary bases, known as multi-bit networks (MBNs), which accelerate the inference and reduce the storage for the deployment on…

We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…

We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…

With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions…

Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…

Quantization is widely employed in both cloud and edge systems to reduce the memory occupation, latency, and energy consumption of deep neural networks. In particular, mixed-precision quantization, i.e., the use of different bit-widths for…

A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often the variability of…

Simulating interactions between deformable bodies is vital in fields like material science, mechanical design, and robotics. While learning-based methods with Graph Neural Networks (GNNs) are effective at solving complex physical systems,…

In isogeometric analysis, isogeometric function spaces are employed for accurately representing the solution to a partial differential equation (PDE) on a parameterized domain. They are generated from a tensor-product spline space by…

Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…