Related papers: Diffeomorphic Neural Operator Learning
Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural…
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational and structural challenges for standard data-driven…
While current deep learning models achieve high performance by learning statistical correlations from vast datasets,which stands in stark contrast to human learning. They lack the flexibility of humans-particularly preverbal infants-to…
Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is…
Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…
Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost…
In this paper, we propose a novel mathematical framework for piecewise diffeomorphic image registration that involves discontinuous sliding motion using a diffeomorphism groupoid and algebroid approach. The traditional Large Deformation…
In this study, we build upon a previously proposed neuroevolution framework to evolve deep convolutional models. Specifically, the genome encoding and the crossover operator are extended to make them applicable to layered networks. We also…
Deep Neural Networks (DNNs) are generated by sequentially performing linear and non-linear processes. Using a combination of linear and non-linear procedures is critical for generating a sufficiently deep feature space. The majority of…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
We hypothesize that a key bottleneck in generalizable robot manipulation is not solely data scale or policy capacity, but a structural mismatch between current visual backbones and the physical requirements of closed-loop control. While…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly…
We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…
State-of-the-art fully intrinsic networks for non-rigid shape matching often struggle to disambiguate the symmetries of the shapes leading to unstable correspondence predictions. Meanwhile, recent advances in the functional map framework…
This work proposes a multimodal diffeomorphic registration method using Neural Ordinary Differential Equations (Neural ODEs). Nonrigid registration algorithms exhibit tradeoffs between their accuracy, the computational complexity of their…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
The diffusion bridge, which is a diffusion process conditioned on hitting a specific state within a finite period, has found broad applications in various scientific and engineering fields. However, simulating diffusion bridges for modeling…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…