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Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…
Medical image segmentation requires large annotated datasets, creating a significant bottleneck for clinical applications. While few-shot segmentation methods can learn from minimal examples, existing approaches demonstrate suboptimal…
Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…
Surface defect inspection is an important task in industrial inspection. Deep learning-based methods have demonstrated promising performance in this domain. Nevertheless, these methods still suffer from misjudgment when encountering…
Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…
Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…
We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still…
Semantic segmentation is pixel-wise classification which retains critical spatial information. The "feature map reuse" has been commonly adopted in CNN based approaches to take advantage of feature maps in the early layers for the later…
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…
Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…
In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…
We present DeepVekua, a hybrid architecture that unifies geometric deep learning with spectral analysis to solve partial differential equations (PDEs) in sparse data regimes. By learning a diffeomorphic coordinate transformation that maps…
Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with…
Existing learning-based methods effectively reconstruct HDR images from multi-exposure LDR inputs with extended dynamic range and improved detail, but they rely more on empirical design rather than theoretical foundation, which can impact…