Partial differential equations (PDEs) are an essential modeling tool in engineering and physical sciences. The numerical methods used for solving the more descriptive and sophisticated of these models comprise many computationally expensive modules. Machine learning (ML) provides a way of replacing some of these modules by surrogates that are much more efficient at the time of inference. The resulting PDE-ML coupled systems, however, can be highly susceptible to instabilities [1-3]. Efforts towards ameliorating these have mostly concentrated on improving the accuracy of the surrogates, imbuing them with additional structure, or introducing problem-specific stabilizers, and have garnered limited success [4-7]. In this article, we study a prototype problem to understand the mathematical subtleties involved in PDE-ML coupling, and draw insights that can help with more complex systems.

We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research.

Climate models play a critical role in understanding and projecting climate change. Due to their complexity, their horizontal resolution of ~40-100 km remains too coarse to resolve processes such as clouds and convection, which need to be approximated via parameterizations. These parameterizations are a major source of systematic errors and large uncertainties in climate projections. Deep learning (DL)-based parameterizations, trained on computationally expensive, short high-resolution simulations, have shown great promise for improving climate models in that regard. However, their lack of interpretability and tendency to learn spurious non-physical correlations result in reduced trust in the climate simulation. We propose an efficient supervised learning framework for DL-based parameterizations that leads to physically consistent models with improved interpretability and negligible computational overhead compared to standard supervised training. First, key features determining the target physical processes are uncovered. Subsequently, the neural network is fine-tuned using only those relevant features. We show empirically that our method robustly identifies a small subset of the inputs as actual physical drivers, therefore, removing spurious non-physical relationships. This results in by design physically consistent and interpretable neural networks while maintaining the predictive performance of standard black-box DL-based parameterizations. Our framework represents a crucial step in addressing a major challenge in data-driven climate model parameterizations by respecting the underlying physical processes, and may also benefit physically consistent deep learning in other research fields.

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints. A consequence is inaccurate and imprecise predictions of critical processes such as storms. Hybrid methods that combine physics with machine learning (ML) have introduced a new generation of higher fidelity climate simulators that can sidestep Moore's Law by outsourcing compute-hungry, short, high-resolution simulations to ML emulators. However, this hybrid ML-physics simulation approach requires domain-specific treatment and has been inaccessible to ML experts because of lack of training data and relevant, easy-to-use workflows. We present ClimSim, the largest-ever dataset designed for hybrid ML-physics research. It comprises multi-scale climate simulations, developed by a consortium of climate scientists and ML researchers. It consists of 5.7 billion pairs of multivariate input and output vectors that isolate the influence of locally-nested, high-resolution, high-fidelity physics on a host climate simulator's macro-scale physical state. The dataset is global in coverage, spans multiple years at high sampling frequency, and is designed such that resulting emulators are compatible with downstream coupling into operational climate simulators. We implement a range of deterministic and stochastic regression baselines to highlight the ML challenges and their scoring.

An amateur photographer who goes by the name "ibreakphotos" decided to do an experiment on his Samsung phone last month to find out how a feature called "space zoom" actually works. The feature, first released in 2020, claims a 100x zoom rate, and Samsung used sparkling clear images of the Moon in its marketing. Ibreakphotos took his own pictures of the Moon--blurry and without detail--and watched as his phone added craters and other details. The phone's artificial intelligence software was using data from its "training" on many other pictures of the Moon to add detail where there was none. "The Moon pictures from Samsung are fake," he wrote, leading many to wonder whether the shots people take are really theirs anymore--or if they can even be described as photographs. Samsung has defended the technology, saying it does not "overlay" images, and pointed out that users can switch off the function.

This is the consensus view of an MIT Technology Review Insights survey of 210 members of technology executives, conducted in March 2021. These respondents report that they need--and still often lack-- the ability to develop new digital channels and services quickly, and to optimize them in real time. Underpinning these waves of digital transformation are two fundamental drivers: the ability to serve and understand customers better, and the need to increase employees' ability to work more effectively toward those goals. Two-thirds of respondents indicated that more efficient customer experience delivery was the most critical objective. This was followed closely by the use of analytics and insight to improve products and services (60%).

Since the pandemic began, the video games industry has been booming. Last year was a bumper year, with most of the world's population forced inside by lockdowns and looking for safe ways to have fun and socialise, and new games consoles such as PlayStation 5 and Xbox Series X/S launching in November. UK consumers spent more on games last year than ever before; Roblox, a gaming platform popular with children and teens, saw an 85% uptick in players and shares in the company recently rose 60%, increasing its value to $47bn. Last year's games were great, too, from lockdown saviour Animal Crossing: New Horizons to the provocative horror game The Last of Us II and the knockabout multiplayer caper Fall Guys. But 2021, so far, is depressingly devoid of exciting gaming experiences.