Laure Zanna

J. Nathan Kutz, Peter Battaglia, Michael Brenner et al.

Machine learning (ML) and artificial intelligence (AI) algorithms are transforming and empowering the characterization and control of dynamic systems in the engineering, physical, and biological sciences. These emerging modeling paradigms require comparative metrics to evaluate a diverse set of scientific objectives, including forecasting, state reconstruction, generalization, and control, while also considering limited data scenarios and noisy measurements. We introduce a common task framework (CTF) for science and engineering, which features a growing collection of challenge data sets with a diverse set of practical and common objectives. The CTF is a critically enabling technology that has contributed to the rapid advance of ML/AI algorithms in traditional applications such as speech recognition, language processing, and computer vision. There is a critical need for the objective metrics of a CTF to compare the diverse algorithms being rapidly developed and deployed in practice today across science and engineering.

Karl Otness, Laure Zanna, Joan Bruna

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable to problems with significant self-similarity or in which the prediction task is challenging and where stability of a learned model's impact on the target dynamical system is important. We evaluate our approach on a climate subgrid parameterization task in which our multiscale networks correct chaotic underlying models to reflect the contributions of unresolved, fine-scale dynamics.

Fabrizio Falasca, Laure Zanna

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of temporally discrete trajectories. We then impose causal constraints to suppress spurious interactions across degrees of freedom. The resulting neural models accurately capture stationary statistics and responses to both small and large external forcings. We demonstrate the framework on the stochastic Charney-DeVore equations and on a symmetry-broken Lorenz-96 system. The framework is broadly applicable to reduced-order modeling of turbulent dynamical systems from observational data.

Surya Dheeshjith, Adam Subel, Alistair Adcroft et al.

AI emulators for forecasting have emerged as powerful tools that can outperform conventional numerical predictions. The next frontier is to build emulators for long climate simulations with skill across a range of spatiotemporal scales, a particularly important goal for the ocean. Our work builds a skillful global emulator of the ocean component of a state-of-the-art climate model. We emulate key ocean variables, sea surface height, horizontal velocities, temperature, and salinity, across their full depth. We use a modified ConvNeXt UNet architecture trained on multi-depth levels of ocean data. We show that the ocean emulator - Samudra - which exhibits no drift relative to the truth, can reproduce the depth structure of ocean variables and their interannual variability. Samudra is stable for centuries and 150 times faster than the original ocean model. Samudra struggles to capture the correct magnitude of the forcing trends and simultaneously remain stable, requiring further work.

James P. C. Duncan, Elynn Wu, Surya Dheeshjith et al. · allen-ai

Traditional numerical global climate models simulate the full Earth system by exchanging boundary conditions between separate simulators of the atmosphere, ocean, sea ice, land surface, and other geophysical processes. This paradigm allows for distributed development of individual components within a common framework, unified by a coupler that handles translation between realms via spatial or temporal alignment and flux exchange. Following a similar approach adapted for machine learning-based emulators, we present SamudrACE: a coupled global climate model emulator which produces centuries-long simulations at 1-degree horizontal, 6-hourly atmospheric, and 5-daily oceanic resolution, with 145 2D fields spanning 8 atmospheric and 19 oceanic vertical levels, plus sea ice, surface, and top-of-atmosphere variables. SamudrACE is highly stable and has low climate biases comparable to those of its components with prescribed boundary forcing, with realistic variability in coupled climate phenomena such as ENSO that is not possible to simulate in uncoupled mode.

Moein Darman, Pedram Hassanzadeh, Laure Zanna et al.

Transfer learning (TL) is a powerful tool for enhancing the performance of neural networks (NNs) in applications such as weather and climate prediction and turbulence modeling. TL enables models to generalize to out-of-distribution data with minimal training data from the new system. In this study, we employ a 9-layer convolutional NN to predict the subgrid forcing in a two-layer ocean quasi-geostrophic system and examine which metrics best describe its performance and generalizability to unseen dynamical regimes. Fourier analysis of the NN kernels reveals that they learn low-pass, Gabor, and high-pass filters, regardless of whether the training data are isotropic or anisotropic. By analyzing the activation spectra, we identify why NNs fail to generalize without TL and how TL can overcome these limitations: the learned weights and biases from one dataset underestimate the out-of-distribution sample spectra as they pass through the network, leading to an underestimation of output spectra. By re-training only one layer with data from the target system, this underestimation is corrected, enabling the NN to produce predictions that match the target spectra. These findings are broadly applicable to data-driven parameterization of dynamical systems.

William Gregory, Mitchell Bushuk, James Duncan et al.

We introduce FloeNet, a machine-learning emulator trained on the Geophysical Fluid Dynamics Laboratory global sea ice model, SIS2. FloeNet is a mass-conserving model, emulating 6-hour mass and area budget tendencies related to sea ice and snow-on-sea-ice growth, melt, and advection. We train FloeNet using simulated data from a reanalysis-forced ice-ocean simulation and test its ability to generalize to pre-industrial control and 1% CO2 climates. FloeNet outperforms a non-conservative model at reproducing sea ice and snow-on-sea-ice mean state, trends, and inter-annual variability, with volume anomaly correlations above 0.96 in the Antarctic and 0.76 in the Arctic, across all forcings. FloeNet also produces the correct thermodynamic vs dynamic response to forcing, enabling physical interpretability of emulator output. Finally, we show that FloeNet outputs high-fidelity coupling-related variables, including ice-surface skin temperature, ice-to-ocean salt flux, and melting energy fluxes. We hypothesize that FloeNet will improve polar climate processes within existing atmosphere and ocean emulators.

Jiarong Wu, Pavel Perezhogin, David John Gagne et al.

Accurately quantifying air-sea fluxes is important for understanding air-sea interactions and improving coupled weather and climate systems. This study introduces a probabilistic framework to represent the highly variable nature of air-sea fluxes, which is missing in deterministic bulk algorithms. Assuming Gaussian distributions conditioned on the input variables, we use artificial neural networks and eddy-covariance measurement data to estimate the mean and variance by minimizing negative log-likelihood loss. The trained neural networks provide alternative mean flux estimates to existing bulk algorithms, and quantify the uncertainty around the mean estimates. Stochastic parameterization of air-sea turbulent fluxes can be constructed by sampling from the predicted distributions. Tests in a single-column forced upper-ocean model suggest that changes in flux algorithms influence sea surface temperature and mixed layer depth seasonally. The ensemble spread in stochastic runs is most pronounced during spring restratification.

Qidong Yang, Weicheng Zhu, Joseph Keslin et al.

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the prediction (instead of just determining the most likely sequence, as in language modeling). In this paper, we propose a Monte Carlo framework to estimate probabilities and confidence intervals associated with the distribution of a discrete sequence. Our framework uses a Monte Carlo simulator, implemented as an autoregressively trained neural network, to sample sequences conditioned on an image input. We then use these samples to estimate the probabilities and confidence intervals. Experiments on synthetic and real data show that the framework produces accurate discriminative predictions, but can suffer from miscalibration. In order to address this shortcoming, we propose a time-dependent regularization method, which is shown to produce calibrated predictions.

Gustau Camps-Valls, Andreas Gerhardus, Urmi Ninad et al.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Sheng Liu, Aakash Kaku, Weicheng Zhu et al.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.