Related papers: Inducing Point Operator Transformer: A Flexible an…

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…

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…

Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Transformer-based models have significantly advanced natural language processing and computer vision in recent years. However, due to the irregular and disordered structure of point cloud data, transformer-based models for 3D deep learning…

We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Data-driven machine learning approaches are being increasingly used to solve partial differential equations (PDEs). They have shown particularly striking successes when training an operator, which takes as input a PDE in some family, and…

Modern compilers optimize programs through a sequence of modular passes over intermediate representations (IR). While this pass-by-pass paradigm offers engineering benefits, it suffers from a pass coordination problem: locally beneficial…

In this work, we present Point Transformer, a deep neural network that operates directly on unordered and unstructured point sets. We design Point Transformer to extract local and global features and relate both representations by…

Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…

Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…

A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the…

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…

In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…

The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained…

Distributed Complex Event Processing (DCEP) is a commonly used paradigm to detect and act on situational changes of many applications, including the Internet of Things (IoT). DCEP achieves this using a simple specification of analytical…

Shape assembly, which aims to reassemble separate parts into a complete object, has gained significant interest in recent years. Existing methods primarily rely on networks to predict the poses of individual parts, but often fail to…

Due to the unaffordable size and intensive computation costs of low-level vision models, All-in-One models that are designed to address a handful of low-level vision tasks simultaneously have been popular. However, existing All-in-One…

In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar, for which standard MATLAB matrix operation syntax (e.g.…