Group Equivariant Fourier Neural Operators for Partial Differential Equations

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable to encode such symmetries in the neural operator architecture for better performance and easier learning. While encoding symmetries in the physical domain using group theory has been studied extensively, how to capture symmetries in the frequency domain is under-explored. In this work, we extend group convolutions to the frequency domain and design Fourier layers that are equivariant to rotations, translations, and reflections by leveraging the equivariance property of the Fourier transform. The resulting $G$-FNO architecture generalizes well across input resolutions and performs well in settings with varying levels of symmetry. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).Comment: Proceedings of the 40th International Conference on Machine Learning https://icml.cc/virtual/2023/poster/2387

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science

Elevated Serum Free Light Chains Are Associated With Event-Free and Overall Survival in Two Independent Cohorts of Patients With Diffuse Large B-Cell Lymphoma

Purpose The serum free light chain (FLC) assay quantitates free kappa (κ) and free lambda (γ) immunoglobulin light chains. This assay has prognostic value in plasma cell proliferative disorders. There are limited data on serum FLC in B-cell malignancies. Patients and MethodsThe association of pretreatment FLC with event-free survival (EFS) and overall survival (OS) in diffuse large B-cell lymphoma (DLBCL) was evaluated in 76 patients from the North Central Cancer Treatment Group trial N0489 (NCT00301821) and 219 patients from the University of Iowa/Mayo Clinic Specialized Program of Research Excellence Molecular Epidemiology Resource (MER). Published reference ranges were used to define an elevated FLC or an abnormal κ:γ FLC ratio. Results Elevated FLC or abnormal κ:γ FLC ratio was present in 32% and 14% of patients, respectively. Patients with elevated FLC had an inferior OS and EFS in both cohorts compared with patients with normal FLC (N0489: EFS hazard ratio [HR], 3.06; OS HR, 3.16; both P \u3c .02; MER: EFS HR, 2.42; OS HR, 3.40; both P \u3c .001; combined EFS HR, 2.57; OS HR, 3.74; both P \u3c .001). All associations remained significant for EFS and OS after adjusting for the International Prognostic Index (IPI). Abnormal κ:γ FLC ratio was modestly associated with outcome in the combined group (EFS HR, 1.61; OS HR, 1.67; both P = .07), but not in patients without corresponding elevated κ or γ. Elevated FLC was the strongest predictor of outcome in multivariable models with the IPI components. Conclusion Increased serum FLC is an independent, adverse prognostic factor for EFS and OS in DLBCL and warrants further evaluation as a biomarker in DLBCL. Copyright © 2011 American Society of Clinical Oncology