Learning skillful medium-range global weather forecasting.

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy but does not directly use historical weather data to improve the underlying model. Here, we introduce GraphCast, a machine learning-based method trained directly from reanalysis data. It predicts hundreds of weather variables for the next 10 days at 0.25° resolution globally in under 1 minute. GraphCast significantly outperforms the most accurate operational deterministic systems on 90% of 1380 verification targets, and its forecasts support better severe event prediction, including tropical cyclone tracking, atmospheric rivers, and extreme temperatures. GraphCast is a key advance in accurate and efficient weather forecasting and helps realize the promise of machine learning for modeling complex dynamical systems.

Toward accelerated data-driven Rayleigh-Bénard convection simulations.

A hybrid data-driven/finite volume method for 2D and 3D thermal convective flows is introduced. The approach relies on a single-step loss, convolutional neural network that is active only in the near-wall region of the flow. We demonstrate that the method significantly reduces errors in the prediction of the heat flux over the long-time horizon and increases pointwise accuracy in coarse simulations, when compared to direct computations on the same grids with and without a traditional subgrid model. We trace the success of our machine learning model to the choice of the training procedure, incorporating both the temporal flow development and distributional bias.

Machine learning-accelerated computational fluid dynamics.

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large-eddy simulation, our results are as accurate as baseline solvers with 8 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-fold computational speedups. Our method remains stable during long simulations and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black-box machine-learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.

Machine learning guided aptamer refinement and discovery.

Aptamers are single-stranded nucleic acid ligands that bind to target molecules with high affinity and specificity. They are typically discovered by searching large libraries for sequences with desirable binding properties. These libraries, however, are practically constrained to a fraction of the theoretical sequence space. Machine learning provides an opportunity to intelligently navigate this space to identify high-performing aptamers. Here, we propose an approach that employs particle display (PD) to partition a library of aptamers by affinity, and uses such data to train machine learning models to predict affinity in silico. Our model predicted high-affinity DNA aptamers from experimental candidates at a rate 11-fold higher than random perturbation and generated novel, high-affinity aptamers at a greater rate than observed by PD alone. Our approach also facilitated the design of truncated aptamers 70% shorter and with higher binding affinity (1.5 nM) than the best experimental candidate. This work demonstrates how combining machine learning and physical approaches can be used to expedite the discovery of better diagnostic and therapeutic agents.

Kohn-Sham Equations as Regularizer: Building Prior Knowledge into Machine-Learned Physics.

Including prior knowledge is important for effective machine learning models in physics and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H_{2} dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.

Array programming with NumPy.

Array programming provides a powerful, compact and expressive syntax for accessing, manipulating and operating on data in vectors, matrices and higher-dimensional arrays. NumPy is the primary array programming library for the Python language. It has an essential role in research analysis pipelines in fields as diverse as physics, chemistry, astronomy, geoscience, biology, psychology, materials science, engineering, finance and economics. For example, in astronomy, NumPy was an important part of the software stack used in the discovery of gravitational waves1 and in the first imaging of a black hole2. Here we review how a few fundamental array concepts lead to a simple and powerful programming paradigm for organizing, exploring and analysing scientific data. NumPy is the foundation upon which the scientific Python ecosystem is constructed. It is so pervasive that several projects, targeting audiences with specialized needs, have developed their own NumPy-like interfaces and array objects. Owing to its central position in the ecosystem, NumPy increasingly acts as an interoperability layer between such array computation libraries and, together with its application programming interface (API), provides a flexible framework to support the next decade of scientific and industrial analysis.

Correcting nuisance variation using Wasserstein distance.

Profiling cellular phenotypes from microscopic imaging can provide meaningful biological information resulting from various factors affecting the cells. One motivating application is drug development: morphological cell features can be captured from images, from which similarities between different drug compounds applied at different doses can be quantified. The general approach is to find a function mapping the images to an embedding space of manageable dimensionality whose geometry captures relevant features of the input images. An important known issue for such methods is separating relevant biological signal from nuisance variation. For example, the embedding vectors tend to be more correlated for cells that were cultured and imaged during the same week than for those from different weeks, despite having identical drug compounds applied in both cases. In this case, the particular batch in which a set of experiments were conducted constitutes the domain of the data; an ideal set of image embeddings should contain only the relevant biological information (e.g., drug effects). We develop a general framework for adjusting the image embeddings in order to "forget" domain-specific information while preserving relevant biological information. To achieve this, we minimize a loss function based on distances between marginal distributions (such as the Wasserstein distance) of embeddings across domains for each replicated treatment. For the dataset we present results with, the only replicated treatment happens to be the negative control treatment, for which we do not expect any treatment-induced cell morphology changes. We find that for our transformed embeddings (i) the underlying geometric structure is not only preserved but the embeddings also carry improved biological signal; and (ii) less domain-specific information is present.

Free-Form Diffractive Metagrating Design Based on Generative Adversarial Networks.

A key challenge in metasurface design is the development of algorithms that can effectively and efficiently produce high-performance devices. Design methods based on iterative optimization can push the performance limits of metasurfaces, but they require extensive computational resources that limit their implementation to small numbers of microscale devices. We show that generative neural networks can train from images of periodic, topology-optimized metagratings to produce high-efficiency, topologically complex devices operating over a broad range of deflection angles and wavelengths. Further iterative optimization of these designs yields devices with enhanced robustness and efficiencies, and these devices can be utilized as additional training data for network refinement. In this manner, generative networks can be trained, with a one-time computation cost, and used as a design tool to facilitate the production of near-optimal, topologically complex device designs. We envision that such data-driven design methodologies can apply to other physical sciences domains that require the design of functional elements operating across a wide parameter space.

Learning data-driven discretizations for partial differential equations.

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.

Assessing microscope image focus quality with deep learning.

BACKGROUND: Large image datasets acquired on automated microscopes typically have some fraction of low quality, out-of-focus images, despite the use of hardware autofocus systems. Identification of these images using automated image analysis with high accuracy is important for obtaining a clean, unbiased image dataset. Complicating this task is the fact that image focus quality is only well-defined in foreground regions of images, and as a result, most previous approaches only enable a computation of the relative difference in quality between two or more images, rather than an absolute measure of quality. RESULTS: We present a deep neural network model capable of predicting an absolute measure of image focus on a single image in isolation, without any user-specified parameters. The model operates at the image-patch level, and also outputs a measure of prediction certainty, enabling interpretable predictions. The model was trained on only 384 in-focus Hoechst (nuclei) stain images of U2OS cells, which were synthetically defocused to one of 11 absolute defocus levels during training. The trained model can generalize on previously unseen real Hoechst stain images, identifying the absolute image focus to within one defocus level (approximately 3 pixel blur diameter difference) with 95% accuracy. On a simpler binary in/out-of-focus classification task, the trained model outperforms previous approaches on both Hoechst and Phalloidin (actin) stain images (F-scores of 0.89 and 0.86, respectively over 0.84 and 0.83), despite only having been presented Hoechst stain images during training. Lastly, we observe qualitatively that the model generalizes to two additional stains, Hoechst and Tubulin, of an unseen cell type (Human MCF-7) acquired on a different instrument. CONCLUSIONS: Our deep neural network enables classification of out-of-focus microscope images with both higher accuracy and greater precision than previous approaches via interpretable patch-level focus and certainty predictions. The use of synthetically defocused images precludes the need for a manually annotated training dataset. The model also generalizes to different image and cell types. The framework for model training and image prediction is available as a free software library and the pre-trained model is available for immediate use in Fiji (ImageJ) and CellProfiler.

Generalized master equation with non-Markovian multichromophoric Förster resonance energy transfer for modular exciton densities.

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately described by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.

Inverting pump-probe spectroscopy for state tomography of excitonic systems.

We propose a two-step protocol for inverting ultrafast spectroscopy experiments on a molecular aggregate to extract the time-evolution of the excited state density matrix. The first step is a deconvolution of the experimental signal to determine a pump-dependent response function. The second step inverts this response function to obtain the quantum state of the system, given a model for how the system evolves following the probe interaction. We demonstrate this inversion analytically and numerically for a dimer model system, and evaluate the feasibility of scaling it to larger molecular aggregates such as photosynthetic protein-pigment complexes. Our scheme provides a direct alternative to the approach of determining all Hamiltonian parameters and then simulating excited state dynamics.

Spatial propagation of excitonic coherence enables ratcheted energy transfer.

Experimental evidence shows that a variety of photosynthetic systems can preserve quantum beats in the process of electronic energy transfer, even at room temperature. However, whether this quantum coherence arises in vivo and whether it has any biological function have remained unclear. Here we present a theoretical model that suggests that the creation and recreation of coherence under natural conditions is ubiquitous. Our model allows us to theoretically demonstrate a mechanism for a ratchet effect enabled by quantum coherence, in a design inspired by an energy transfer pathway in the Fenna-Matthews-Olson complex of the green sulfur bacteria. This suggests a possible biological role for coherent oscillations in spatially directing energy transfer. Our results emphasize the importance of analyzing long-range energy transfer in terms of transfer between intercomplex coupling states rather than between site or exciton states.