arXiv subjects

Boris Bonev

Publications and source records attributed to Boris Bonev.

30 records · Page 2Linked to original sources

arXiv2024

A Practical Probabilistic Benchmark for AI Weather Models

Since the weather is chaotic, forecasts aim to predict the distribution of future states rather than make a single prediction. Recently, multiple data driven weather models have emerged claiming breakthroughs in skill. However, these have mostly been benchmarked using deterministic skill scores, and little is known about their probabilistic skill. Unfortunately, it is hard to fairly compare AI weather models in a probabilistic sense, since variations in choice of ensemble initialization, definition of state, and noise injection methodology become confounding. Moreover, even obtaining ensemble forecast baselines is a substantial engineering challenge given the data volumes involved. We sidestep both problems by applying a decades-old idea -- lagged ensembles -- whereby an ensemble can be constructed from a moderately-sized library of deterministic forecasts. This allows the first parameter-free intercomparison of leading AI weather models' probabilistic skill against an operational baseline. The results reveal that two leading AI weather models, i.e. GraphCast and Pangu, are tied on the probabilistic CRPS metric even though the former outperforms the latter in deterministic scoring. We also reveal how multiple time-step loss functions, which many data-driven weather models have employed, are counter-productive: they improve deterministic metrics at the cost of increased dissipation, deteriorating probabilistic skill. This is confirmed through ablations applied to a spherical Fourier Neural Operator (SFNO) approach to AI weather forecasting. Separate SFNO ablations modulating effective resolution reveal it has a useful effect on ensemble dispersion relevant to achieving good ensemble calibration. We hope these and forthcoming insights from lagged ensembles can help guide the development of AI weather forecasts and have thus shared the diagnostic code.

physics.ao-ph↗

arXiv2024

Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-Bénard convection, we found CoDA-NO to outperform existing methods by over 36%.

cs.LG↗

arXiv2024

Modulated Adaptive Fourier Neural Operators for Temporal Interpolation of Weather Forecasts

Weather and climate data are often available at limited temporal resolution, either due to storage limitations, or in the case of weather forecast models based on deep learning, their inherently long time steps. The coarse temporal resolution makes it difficult to capture rapidly evolving weather events. To address this limitation, we introduce an interpolation model that reconstructs the atmospheric state between two points in time for which the state is known. The model makes use of a novel network layer that modifies the adaptive Fourier neural operator (AFNO), which has been previously used in weather prediction and other applications of machine learning to physics problems. The modulated AFNO (ModAFNO) layer takes an embedding, here computed from the interpolation target time, as an additional input and applies a learned shift-scale operation inside the AFNO layers to adapt them to the target time. Thus, one model can be used to produce all intermediate time steps. Trained to interpolate between two time steps 6 h apart, the ModAFNO-based interpolation model produces 1 h resolution intermediate time steps that are visually nearly indistinguishable from the actual corresponding 1 h resolution data. The model reduces the RMSE loss of reconstructing the intermediate steps by approximately 50% compared to linear interpolation. We also demonstrate its ability to reproduce the statistics of extreme weather events such as hurricanes and heat waves better than 6 h resolution data. The ModAFNO layer is generic and is expected to be applicable to other problems, including weather forecasting with tunable lead time.

physics.ao-ph↗

arXiv2024

Exploring the design space of deep-learning-based weather forecasting systems

Despite tremendous progress in developing deep-learning-based weather forecasting systems, their design space, including the impact of different design choices, is yet to be well understood. This paper aims to fill this knowledge gap by systematically analyzing these choices including architecture, problem formulation, pretraining scheme, use of image-based pretrained models, loss functions, noise injection, multi-step inputs, additional static masks, multi-step finetuning (including larger stride models), as well as training on a larger dataset. We study fixed-grid architectures such as UNet, fully convolutional architectures, and transformer-based models, along with grid-invariant architectures, including graph-based and operator-based models. Our results show that fixed-grid architectures outperform grid-invariant architectures, indicating a need for further architectural developments in grid-invariant models such as neural operators. We therefore propose a hybrid system that combines the strong performance of fixed-grid models with the flexibility of grid-invariant architectures. We further show that multi-step fine-tuning is essential for most deep-learning models to work well in practice, which has been a common practice in the past. Pretraining objectives degrade performance in comparison to supervised training, while image-based pretrained models provide useful inductive biases in some cases in comparison to training the model from scratch. Interestingly, we see a strong positive effect of using a larger dataset when training a smaller model as compared to training on a smaller dataset for longer. Larger models, on the other hand, primarily benefit from just an increase in the computational budget. We believe that these results will aid in the design of better weather forecasting systems in the future.

cs.LG↗

arXiv2024

Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh

We present a parsimonious deep learning weather prediction model to forecast seven atmospheric variables with 3-h time resolution for up to one-year lead times on a 110-km global mesh using the Hierarchical Equal Area isoLatitude Pixelization (HEALPix). In comparison to state-of-the-art (SOTA) machine learning (ML) weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at one-week lead times, its skill is only about one day behind both SOTA ML forecast models and the SOTA numerical weather prediction model from the European Centre for Medium-Range Weather Forecasts. We report several improvements in model design, including switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that successfully propagate weather patterns across the globe without requiring separate kernels for the polar and equatorial faces of the cube sphere. Without any loss of spectral power after the first two days, the model can be unrolled autoregressively for hundreds of steps into the future to generate realistic states of the atmosphere that respect seasonal trends, as showcased in one-year simulations.

physics.ao-ph↗

arXiv2024

Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model

Seasonal climate forecasts are socioeconomically important for managing the impacts of extreme weather events and for planning in sectors like agriculture and energy. Climate predictability on seasonal timescales is tied to boundary effects of the ocean on the atmosphere and coupled interactions in the ocean-atmosphere system. We present the Ocean-linked-atmosphere (Ola) model, a high-resolution (0.25°) Artificial Intelligence/ Machine Learning (AI/ML) coupled earth-system model which separately models the ocean and atmosphere dynamics using an autoregressive Spherical Fourier Neural Operator architecture, with a view towards enabling fast, accurate, large ensemble forecasts on the seasonal timescale. We find that Ola exhibits learned characteristics of ocean-atmosphere coupled dynamics including tropical oceanic waves with appropriate phase speeds, and an internally generated El Niño/Southern Oscillation (ENSO) having realistic amplitude, geographic structure, and vertical structure within the ocean mixed layer. We present initial evidence of skill in forecasting the ENSO which compares favorably to the SPEAR model of the Geophysical Fluid Dynamics Laboratory.

physics.ao-ph↗

arXiv2024

Neural Operators with Localized Integral and Differential Kernels

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

cs.LG↗

arXiv2024

Guaranteed Approximation Bounds for Mixed-Precision Neural Operators

Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, many real-world problems require high-resolution training data, and the training time and limited GPU memory pose big barriers. One solution is to train neural operators in mixed precision to reduce the memory requirement and increase training speed. However, existing mixed-precision training techniques are designed for standard neural networks, and we find that their direct application to FNO leads to numerical overflow and poor memory efficiency. Further, at first glance, it may appear that mixed precision in FNO will lead to drastic accuracy degradation since reducing the precision of the Fourier transform yields poor results in classical numerical solvers. We show that this is not the case; in fact, we prove that reducing the precision in FNO still guarantees a good approximation bound, when done in a targeted manner. Specifically, we build on the intuition that neural operator learning inherently induces an approximation error, arising from discretizing the infinite-dimensional ground-truth input function, implying that training in full precision is not needed. We formalize this intuition by rigorously characterizing the approximation and precision errors of FNO and bounding these errors for general input functions. We prove that the precision error is asymptotically comparable to the approximation error. Based on this, we design a simple method to optimize the memory-intensive half-precision tensor contractions by greedily finding the optimal contraction order. Through extensive experiments on different state-of-the-art neural operators, datasets, and GPUs, we demonstrate that our approach reduces GPU memory usage by up to 50% and improves throughput by 58% with little or no reduction in accuracy.

cs.LG↗

arXiv2023

ACE: A fast, skillful learned global atmospheric model for climate prediction

Existing ML-based atmospheric models are not suitable for climate prediction, which requires long-term stability and physical consistency. We present ACE (AI2 Climate Emulator), a 200M-parameter, autoregressive machine learning emulator of an existing comprehensive 100-km resolution global atmospheric model. The formulation of ACE allows evaluation of physical laws such as the conservation of mass and moisture. The emulator is stable for 100 years, nearly conserves column moisture without explicit constraints and faithfully reproduces the reference model's climate, outperforming a challenging baseline on over 90% of tracked variables. ACE requires nearly 100x less wall clock time and is 100x more energy efficient than the reference model using typically available resources. Without fine-tuning, ACE can stably generalize to a previously unseen historical sea surface temperature dataset.

physics.ao-ph↗

arXiv2023

Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

cs.LG↗

arXiv2021

A hierarchical preconditioner for wave problems in quasilinear complexity

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property that Schur complements arising in such problems can be well approximated by hierarchical matrices. An approximate factorization can be computed matrix-free and in a (quasi-)linear number of operations. The nested dissection is specifically designed to aid the factorization process using hierarchical matrices. We demonstrate the viability of the preconditioner on a range of 2D problems, including the Helmholtz equation and the elastic wave equation. Throughout all tests, including wave phenomena with high wavenumbers, the generalized minimal residual method (GMRES) with the proposed preconditioner converges in a very low number of iterations. We demonstrate that this is due to the hierarchical nature of our approach which makes the high wavenumber limit manageable.

math.NA↗

arXiv2019

Generating Liquid Simulations with Deformation-aware Neural Networks

We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach.

cs.GR↗