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Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of…
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…
We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
Video inpainting is the task of filling a region in a video in a visually convincing manner. It is very challenging due to the high dimensionality of the data and the temporal consistency required for obtaining convincing results. Recently,…
Using a layered representation for motion estimation has the advantage of being able to cope with discontinuities and occlusions. In this paper, we learn to estimate optical flow by combining a layered motion representation with deep…
Diffusion models (DMs) have recently been introduced as a regularizing prior for PET image reconstruction, integrating DMs trained on high-quality PET images with unsupervised schemes that condition on measured data. While these approaches…
Physics-informed neural networks (PINNs) are increasingly employed to replace/augment traditional numerical methods in solving partial differential equations (PDEs). While state-of-the-art PINNs have many attractive features, they…
Deep learning-based image generation has seen significant advancements with diffusion models, notably improving the quality of generated images. Despite these developments, generating images with unseen characteristics beneficial for…
Diffusion-based inpainting is a powerful tool for the reconstruction of images from sparse data. Its quality strongly depends on the choice of known data. Optimising their spatial location -- the inpainting mask -- is challenging. A…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
With the growing interest in foundation models for brain signals, graph-based pretraining has emerged as a promising paradigm for learning transferable representations from connectome data. However, existing contrastive and masked…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several…
In this paper, we address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…
We present two novel generative geometric deep learning frameworks, termed Flow Matching PointNet and Diffusion PointNet, for predicting fluid flow variables on irregular geometries by incorporating PointNet into flow matching and diffusion…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…