Related papers: Hermite-NGP: Gradient-Augmented Hash Encoding for …
Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for…
Neural Stochastic Differential Equations (Neural SDEs) provide a principled framework for modeling continuous-time stochastic processes and have been widely adopted in fields ranging from physics to finance. Recent advances suggest that…
A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value…
Instant-NGP has been the state-of-the-art architecture of neural fields in recent years. Its incredible signal-fitting capabilities are generally attributed to its multi-resolution hash grid structure and have been used and improved in…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
Multi-resolution hash encoding has recently been proposed to reduce the computational cost of neural renderings, such as NeRF. This method requires accurate camera poses for the neural renderings of given scenes. However, contrary to…
This paper presents NGP-RT, a novel approach for enhancing the rendering speed of Instant-NGP to achieve real-time novel view synthesis. As a classic NeRF-based method, Instant-NGP stores implicit features in multi-level grids or hash…
This paper presents a novel natural gradient and Hessian-free (NGHF) optimisation framework for neural network training that can operate efficiently in a distributed manner. It relies on the linear conjugate gradient (CG) algorithm to…
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method…
Physics-informed neural networks (PINNs) have attracted a lot of attention in scientific computing as their functional representation of partial differential equation (PDE) solutions offers flexibility and accuracy features. However, their…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
Recently, many works have been proposed to utilize the neural radiance field for novel view synthesis of human performers. However, most of these methods require hours of training, making them difficult for practical use. To address this…
In this paper, a meshless Hermite-HDMR finite difference method is proposed to solve high-dimensional Dirichlet problems. The approach is based on the local Hermite-HDMR expansion with an additional smoothing technique. First, we introduce…
Large-scale distributed training of deep neural networks results in models with worse generalization performance as a result of the increase in the effective mini-batch size. Previous approaches attempt to address this problem by varying…
Machine-learning interatomic potentials (MLIPs) such as neuroevolution potentials (NEP) combine quantum-mechanical accuracy with computational efficiency significantly accelerate atomistic dynamic simulations. Trained by derivative-free…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in recommender systems. Nevertheless, the process of searching and ranking from a large item corpus usually requires high latency, which limits the widespread…
Transformer-based detectors have advanced small-object detection, but they often remain inefficient and vulnerable to background-induced query noise, which motivates deep decoders to refine low-quality queries. We present HELP…
Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous…
In most of mesh-free methods, the calculation of interactions between sample points or particles is the most time consuming. When we use mesh-free methods with high spatial orders, the order of the time integration should also be high. If…