Comparing and Contrasting Deep Learning Weather Prediction Backbones on Navier-Stokes and Atmospheric Dynamics

Remarkable progress in the development of Deep Learning Weather Prediction (DLWP) models positions them to become competitive with traditional numerical weather prediction (NWP) models. Indeed, a wide number of DLWP architectures -- based on various backbones, including U-Net, Transformer, Graph Neural Network (GNN), and Fourier Neural Operator (FNO) -- have demonstrated their potential at forecasting atmospheric states. However, due to differences in training protocols, forecast horizons, and data choices, it remains unclear which (if any) of these methods and architectures are most suitable for weather forecasting and for future model development. Here, we step back and provide a detailed empirical analysis, under controlled conditions, comparing and contrasting the most prominent DLWP models, along with their backbones. We accomplish this by predicting synthetic two-dimensional incompressible Navier-Stokes and real-world global weather dynamics. In terms of accuracy, memory consumption, and runtime, our results illustrate various tradeoffs. For example, on synthetic data, we observe favorable performance of FNO; and on the real-world WeatherBench dataset, our results demonstrate the suitability of ConvLSTM and SwinTransformer for short-to-mid-ranged forecasts. For long-ranged weather rollouts of up to 365 days, we observe superior stability and physical soundness in architectures that formulate a spherical data representation, i.e., GraphCast and Spherical FNO. In addition, we observe that all of these model backbones ``saturate,'' i.e., none of them exhibit so-called neural scaling, which highlights an important direction for future work on these and related models.

Sharpness-diversity tradeoff: improving flat ensembles with SharpBalance

Recent studies on deep ensembles have identified the sharpness of the local minima of individual learners and the diversity of the ensemble members as key factors in improving test-time performance. Building on this, our study investigates the interplay between sharpness and diversity within deep ensembles, illustrating their crucial role in robust generalization to both in-distribution (ID) and out-of-distribution (OOD) data. We discover a trade-off between sharpness and diversity: minimizing the sharpness in the loss landscape tends to diminish the diversity of individual members within the ensemble, adversely affecting the ensemble's improvement. The trade-off is justified through our theoretical analysis and verified empirically through extensive experiments. To address the issue of reduced diversity, we introduce SharpBalance, a novel training approach that balances sharpness and diversity within ensembles. Theoretically, we show that our training strategy achieves a better sharpness-diversity trade-off. Empirically, we conducted comprehensive evaluations in various data sets (CIFAR-10, CIFAR-100, TinyImageNet) and showed that SharpBalance not only effectively improves the sharpness-diversity trade-off, but also significantly improves ensemble performance in ID and OOD scenarios.

Reliable edge machine learning hardware for scientific applications

Extreme data rate scientific experiments create massive amounts of data that require efficient ML edge processing. This leads to unique validation challenges for VLSI implementations of ML algorithms: enabling bit-accurate functional simulations for performance validation in experimental software frameworks, verifying those ML models are robust under extreme quantization and pruning, and enabling ultra-fine-grained model inspection for efficient fault tolerance. We discuss approaches to developing and validating reliable algorithms at the scientific edge under such strict latency, resource, power, and area requirements in extreme experimental environments. We study metrics for developing robust algorithms, present preliminary results and mitigation strategies, and conclude with an outlook of these and future directions of research towards the longer-term goal of developing autonomous scientific experimentation methods for accelerated scientific discovery.

Recent and Upcoming Developments in Randomized Numerical Linear Algebra for Machine Learning

Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area which uses randomness to develop improved algorithms for ubiquitous matrix problems. The area has reached a certain level of maturity; but recent hardware trends, efforts to incorporate RandNLA algorithms into core numerical libraries, and advances in machine learning, statistics, and random matrix theory, have lead to new theoretical and practical challenges. This article provides a self-contained overview of RandNLA, in light of these developments.

Towards Scalable and Versatile Weight Space Learning

Learning representations of well-trained neural network models holds the promise to provide an understanding of the inner workings of those models. However, previous work has either faced limitations when processing larger networks or was task-specific to either discriminative or generative tasks. This paper introduces the SANE approach to weight-space learning. SANE overcomes previous limitations by learning task-agnostic representations of neural networks that are scalable to larger models of varying architectures and that show capabilities beyond a single task. Our method extends the idea of hyper-representations towards sequential processing of subsets of neural network weights, thus allowing one to embed larger neural networks as a set of tokens into the learned representation space. SANE reveals global model information from layer-wise embeddings, and it can sequentially generate unseen neural network models, which was unattainable with previous hyper-representation learning methods. Extensive empirical evaluation demonstrates that SANE matches or exceeds state-of-the-art performance on several weight representation learning benchmarks, particularly in initialization for new tasks and larger ResNet architectures.

WaveCastNet: An AI-enabled Wavefield Forecasting Framework for Earthquake Early Warning

Large earthquakes can be destructive and quickly wreak havoc on a landscape. To mitigate immediate threats, early warning systems have been developed to alert residents, emergency responders, and critical infrastructure operators seconds to a minute before seismic waves arrive. These warnings provide time to take precautions and prevent damage. The success of these systems relies on fast, accurate predictions of ground motion intensities, which is challenging due to the complex physics of earthquakes, wave propagation, and their intricate spatial and temporal interactions. To improve early warning, we propose a novel AI-enabled framework, WaveCastNet, for forecasting ground motions from large earthquakes. WaveCastNet integrates a novel convolutional Long Expressive Memory (ConvLEM) model into a sequence to sequence (seq2seq) forecasting framework to model long-term dependencies and multi-scale patterns in both space and time. WaveCastNet, which shares weights across spatial and temporal dimensions, requires fewer parameters compared to more resource-intensive models like transformers and thus, in turn, reduces inference times. Importantly, WaveCastNet also generalizes better than transformer-based models to different seismic scenarios, including to more rare and critical situations with higher magnitude earthquakes. Our results using simulated data from the San Francisco Bay Area demonstrate the capability to rapidly predict the intensity and timing of destructive ground motions. Importantly, our proposed approach does not require estimating earthquake magnitudes and epicenters, which are prone to errors using conventional approaches; nor does it require empirical ground motion models, which fail to capture strongly heterogeneous wave propagation effects.

There is HOPE to Avoid HiPPOs for Long-memory State Space Models

State-space models (SSMs) that utilize linear, time-invariant (LTI) systems are known for their effectiveness in learning long sequences. However, these models typically face several challenges: (i) they require specifically designed initializations of the system matrices to achieve state-of-the-art performance, (ii) they require training of state matrices on a logarithmic scale with very small learning rates to prevent instabilities, and (iii) they require the model to have exponentially decaying memory in order to ensure an asymptotically stable LTI system. To address these issues, we view SSMs through the lens of Hankel operator theory, which provides us with a unified theory for the initialization and training of SSMs. Building on this theory, we develop a new parameterization scheme, called HOPE, for LTI systems that utilizes Markov parameters within Hankel operators. This approach allows for random initializations of the LTI systems and helps to improve training stability, while also provides the SSMs with non-decaying memory capabilities. Our model efficiently implements these innovations by nonuniformly sampling the transfer functions of LTI systems, and it requires fewer parameters compared to canonical SSMs. When benchmarked against HiPPO-initialized models such as S4 and S4D, an SSM parameterized by Hankel operators demonstrates improved performance on Long-Range Arena (LRA) tasks. Moreover, we use a sequential CIFAR-10 task with padded noise to empirically corroborate our SSM's long memory capacity.

LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement

Pretrained large language models (LLMs) are currently state-of-the-art for solving the vast majority of natural language processing tasks. While many real-world applications still require fine-tuning to reach satisfactory levels of performance, many of them are in the low-data regime, making fine-tuning challenging. To address this, we propose LLM2LLM, a targeted and iterative data augmentation strategy that uses a teacher LLM to enhance a small seed dataset by augmenting additional data that can be used for fine-tuning on a specific task. LLM2LLM (1) fine-tunes a baseline student LLM on the initial seed data, (2) evaluates and extracts data points that the model gets wrong, and (3) uses a teacher LLM to generate synthetic data based on these incorrect data points, which are then added back into the training data. This approach amplifies the signal from incorrectly predicted data points by the LLM during training and reintegrates them into the dataset to focus on more challenging examples for the LLM. Our results show that LLM2LLM significantly enhances the performance of LLMs in the low-data regime, outperforming both traditional fine-tuning and other data augmentation baselines. LLM2LLM reduces the dependence on labor-intensive data curation and paves the way for more scalable and performant LLM solutions, allowing us to tackle data-constrained domains and tasks. We achieve improvements up to 24.2% on the GSM8K dataset, 32.6% on CaseHOLD, 32.0% on SNIPS, 52.6% on TREC and 39.8% on SST-2 over regular fine-tuning in the low-data regime using a LLaMA2-7B student model.

AI and Memory Wall

The availability of unprecedented unsupervised training data, along with neural scaling laws, has resulted in an unprecedented surge in model size and compute requirements for serving/training LLMs. However, the main performance bottleneck is increasingly shifting to memory bandwidth. Over the past 20 years, peak server hardware FLOPS has been scaling at 3.0x/2yrs, outpacing the growth of DRAM and interconnect bandwidth, which have only scaled at 1.6 and 1.4 times every 2 years, respectively. This disparity has made memory, rather than compute, the primary bottleneck in AI applications, particularly in serving. Here, we analyze encoder and decoder Transformer models and show how memory bandwidth can become the dominant bottleneck for decoder models. We argue for a redesign in model architecture, training, and deployment strategies to overcome this memory limitation.

Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs

Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural Operators (NOs) have emerged as particularly promising. We observe that several uncertainty quantification (UQ) methods for NOs fail for test inputs that are even moderately out-of-domain (OOD), even when the model approximates the solution well for in-domain tasks. To address this limitation, we show that ensembling several NOs can identify high-error regions and provide good uncertainty estimates that are well-correlated with prediction errors. Based on this, we propose a cost-effective alternative, DiverseNO, that mimics the properties of the ensemble by encouraging diverse predictions from its multiple heads in the last feed-forward layer. We then introduce Operator-ProbConserv, a method that uses these well-calibrated UQ estimates within the ProbConserv framework to update the model. Our empirical results show that Operator-ProbConserv enhances OOD model performance for a variety of challenging PDE problems and satisfies physical constraints such as conservation laws.