Related papers: Diffeomorphic Neural Operator Learning
Dynamic graph-level embedding aims to capture structural evolution in networks, which is essential for modeling real-world scenarios. However, existing methods face two critical yet under-explored issues: Structural Visit Bias, where random…
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…
In this work, we propose a disentangled latent optimization-based method for parameterizing grouped deforming 3D objects into shape and deformation factors in an unsupervised manner. Our approach involves the joint optimization of a…
Unsupervised learning enables modeling complex images without the need for annotations. The representation learned by such models can facilitate any subsequent analysis of large image datasets. However, some generative factors that cause…
Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was…
Reaction-diffusion (RD) equations underpin pattern formation across chemistry, biology, and physics, yet learning stable operators that forecast their long-term dynamics from data remains challenging. Neural-operator surrogates provide…
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…
Video-diffusion models have recently set the standard in video generation, inpainting, and domain translation thanks to their training stability and high perceptual fidelity. Building on these strengths, we repurpose conditional video…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…
Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…
Understanding and predicting microstructure evolution is fundamental to materials science, as it governs the resulting properties and performance of materials. Traditional simulation methods, such as phase-field models, offer high-fidelity…
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…
An evolving area of research in deep learning is the study of architectures and inductive biases that support the learning of relational feature representations. In this paper, we address the challenge of learning representations of…
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…
We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…