Jayesh K. Gupta

Johannes Brandstetter, Rianne van den Berg, Max Welling et al.

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Due to the computationally expensive nature of their standard solution methods, neural PDE surrogates have become an active research topic to accelerate these simulations. However, current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated. Viewing the time evolution of such correlated fields through the lens of multivector fields allows us to overcome these limitations. Multivector fields consist of scalar, vector, as well as higher-order components, such as bivectors and trivectors. Their algebraic properties, such as multiplication, addition and other arithmetic operations can be described by Clifford algebras. To our knowledge, this paper presents the first usage of such multivector representations together with Clifford convolutions and Clifford Fourier transforms in the context of deep learning. The resulting Clifford neural layers are universally applicable and will find direct use in the areas of fluid dynamics, weather forecasting, and the modeling of physical systems in general. We empirically evaluate the benefit of Clifford neural layers by replacing convolution and Fourier operations in common neural PDE surrogates by their Clifford counterparts on 2D Navier-Stokes and weather modeling tasks, as well as 3D Maxwell equations. For similar parameter count, Clifford neural layers consistently improve generalization capabilities of the tested neural PDE surrogates. Source code for our PyTorch implementation is available at https://microsoft.github.io/cliffordlayers/.

Jayesh K. Gupta, Johannes Brandstetter

Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical utility of training such surrogates is contingent on their ability to model complex multi-scale spatio-temporal phenomena. Various neural network architectures have been proposed to target such phenomena, most notably Fourier Neural Operators (FNOs), which give a natural handle over local & global spatial information via parameterization of different Fourier modes, and U-Nets which treat local and global information via downsampling and upsampling paths. However, generalizing across different equation parameters or time-scales still remains a challenge. In this work, we make a comprehensive comparison between various FNO, ResNet, and U-Net like approaches to fluid mechanics problems in both vorticity-stream and velocity function form. For U-Nets, we transfer recent architectural improvements from computer vision, most notably from object segmentation and generative modeling. We further analyze the design considerations for using FNO layers to improve performance of U-Net architectures without major degradation of computational cost. Finally, we show promising results on generalization to different PDE parameters and time-scales with a single surrogate model. Source code for our PyTorch benchmark framework is available at https://github.com/microsoft/pdearena.

David Ruhe, Jayesh K. Gupta, Steven de Keninck et al.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable $\textit{geometric templates}$ that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Benoit Guillard, Sai Vemprala, Jayesh K. Gupta et al.

Simulating realistic sensors is a challenging part in data generation for autonomous systems, often involving carefully handcrafted sensor design, scene properties, and physics modeling. To alleviate this, we introduce a pipeline for data-driven simulation of a realistic LiDAR sensor. We propose a model that learns a mapping between RGB images and corresponding LiDAR features such as raydrop or per-point intensities directly from real datasets. We show that our model can learn to encode realistic effects such as dropped points on transparent surfaces or high intensity returns on reflective materials. When applied to naively raycasted point clouds provided by off-the-shelf simulator software, our model enhances the data by predicting intensities and removing points based on the scene's appearance to match a real LiDAR sensor. We use our technique to learn models of two distinct LiDAR sensors and use them to improve simulated LiDAR data accordingly. Through a sample task of vehicle segmentation, we show that enhancing simulated point clouds with our technique improves downstream task performance.

Kunal Menda, Jayesh K. Gupta, Zachary Manchester et al.

Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box parameterization of mechanical systems, typically fit to data by minimizing the error between predicted and observed accelerations or next states. In this work, we propose a methodology for fitting SMMs to data by minimizing the discrete Euler-Lagrange residual. To study our methodology, we fit models to joint-angle time-series from undamped and damped double-pendulums, studying the quality of learned models fit to data with and without observation noise. Experiments show that our methodology learns models that are better in accuracy to those of the conventional schemes for fitting SMMs. We identify use cases in which our method is a more appropriate methodology. Source code for reproducing the experiments is available at https://github.com/sisl/delsmm.

Cristian Bodnar, Raphaël Rousseau-Rizzi, Nikhil Shankar et al.

Weather foundation models (WFMs) have recently set new benchmarks in global forecast skill, yet their concrete value for the weather-sensitive infrastructure that powers modern society remains largely unexplored. In this study, we fine-tune Silurian AI's 1.5B-parameter WFM, Generative Forecasting Transformer (GFT), on a rich archive of Hydro-Québec asset observations--including transmission-line weather stations, wind-farm met-mast streams, and icing sensors--to deliver hyper-local, asset-level forecasts for five grid-critical variables: surface temperature, precipitation, hub-height wind speed, wind-turbine icing risk, and rime-ice accretion on overhead conductors. Across 6-72 h lead times, the tailored model surpasses state-of-the-art NWP benchmarks, trimming temperature mean absolute error (MAE) by 15%, total-precipitation MAE by 35%, and lowering wind speed MAE by 15%. Most importantly, it attains an average precision score of 0.72 for day-ahead rime-ice detection, a capability absent from existing operational systems, which affords several hours of actionable warning for potentially catastrophic outage events. These results show that WFMs, when post-trained with small amounts of high-fidelity, can serve as a practical foundation for next-generation grid-resilience intelligence.

Cristian Bodnar, Wessel P. Bruinsma, Ana Lucic et al.

Reliable forecasts of the Earth system are crucial for human progress and safety from natural disasters. Artificial intelligence offers substantial potential to improve prediction accuracy and computational efficiency in this field, however this remains underexplored in many domains. Here we introduce Aurora, a large-scale foundation model for the Earth system trained on over a million hours of diverse data. Aurora outperforms operational forecasts for air quality, ocean waves, tropical cyclone tracks, and high-resolution weather forecasting at orders of magnitude smaller computational expense than dedicated existing systems. With the ability to fine-tune Aurora to diverse application domains at only modest computational cost, Aurora represents significant progress in making actionable Earth system predictions accessible to anyone.