相关论文: Flowers: A Warp Drive for Neural PDE Solvers

Autoregressive generative PDE solvers can be accurate one step ahead yet drift over long rollouts, especially in coarse-to-fine regimes where each step must regenerate unresolved fine scales. This is the regime of diffusion and…

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

Underground pumped hydro energy storage (UPHES) systems play a critical role in grid-scale energy storage for renewable integration, yet optimal day-ahead scheduling remains computationally prohibitive due to nonlinear turbine performance…

Traffic flow forecasting is a crucial task in intelligent transport systems. Deep learning offers an effective solution, capturing complex patterns in time-series traffic flow data to enable the accurate prediction. However, deep learning…

Multi-modal fusion is of great significance in neuroscience which integrates information from different modalities and can achieve better performance than uni-modal methods in downstream tasks. Current multi-modal fusion methods in brain…

Trainable layers such as convolutional building blocks are the standard network design choices by learning parameters to capture the global context through successive spatial operations. When designing an efficient network, trainable layers…

Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by…

Transformer-based models dominate modern AI workloads but exacerbate memory bottlenecks due to their quadratic attention complexity and ever-growing model sizes. Existing accelerators, such as Groq and Cerebras, mitigate off-chip traffic…

We present a single-layer feedforward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse grained computations such as those encountered in large…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are…

Attention mechanisms, primarily designed to capture pairwise correlations between words, have become the backbone of machine learning, expanding beyond natural language processing into other domains. This growth in adaptation comes at the…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

State-of-the-art neural network models estimate large displacement optical flow in multi-resolution and use warping to propagate the estimation between two resolutions. Despite their impressive results, it is known that there are two…

Learning-based fluid simulation networks have been proven as viable alternatives to traditional numerical solvers for the Navier-Stokes equations. Existing neural methods follow Smoothed Particle Hydrodynamics (SPH) frameworks, which…

Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent…

Like other applications in computer vision, medical image segmentation has been most successfully addressed using deep learning models that rely on the convolution operation as their main building block. Convolutions enjoy important…

Clustering is a core task in machine learning with wide-ranging applications in data mining and pattern recognition. However, its unsupervised nature makes it inherently challenging. Many existing clustering algorithms suffer from critical…

Generating high-dimensional visual modalities is a computationally intensive task. A common solution is progressive generation, where the outputs are synthesized in a coarse-to-fine spectral autoregressive manner. While diffusion models…

We present Walklets, a novel approach for learning multiscale representations of vertices in a network. In contrast to previous works, these representations explicitly encode multiscale vertex relationships in a way that is analytically…