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Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…
Generative modelling has been a topic at the forefront of machine learning research for a substantial amount of time. With the recent success in the field of machine learning, especially in deep learning, there has been an increased…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
Topological solitons, which are stable, localized solutions of nonlinear differential equations, are crucial in various fields of physics and mathematics, including particle physics and cosmology. However, solving these solitons presents…
Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…
Constructive neural combinatorial optimization (NCO) has attracted growing research attention due to its ability to solve complex routing problems without relying on handcrafted rules. However, existing NCO methods face significant…
Constructing a robust model that can effectively generalize to test samples under distribution shifts remains a significant challenge in the field of medical imaging. The foundational models for vision and language, pre-trained on extensive…
The development and evaluation of graph neural networks (GNNs) generally follow the independent and identically distributed (i.i.d.) assumption. Yet this assumption is often untenable in practice due to the uncontrollable data generation…
Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…
We propose a novel-view augmentation (NOVA) strategy to train NeRFs for photo-realistic 3D composition of dynamic objects in a static scene. Compared to prior work, our framework significantly reduces blending artifacts when inserting…
Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This…
Data-driven molecular discovery leverages artificial intelligence/machine learning (AI/ML) and generative modeling to filter and design novel molecules. Discovering novel molecules requires accurate out-of-distribution (OOD) predictions,…
This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…
Deep neural networks achieve superior performance in challenging tasks such as image classification. However, deep classifiers tend to incorrectly classify out-of-distribution (OOD) inputs, which are inputs that do not belong to the…
We study theoretical guarantees for solving linear systems in-context using a linear transformer architecture. For in-domain generalization, we provide neural scaling laws that bound the generalization error in terms of the number of tasks…
Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…
Topology optimization is a critical task in engineering design, where the goal is to optimally distribute material in a given space for maximum performance. We introduce Neural Implicit Topology Optimization (NITO), a novel approach to…