Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work.

We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we derive the minimax optimal (squared) $\ell_2$ estimation error rate, parametrized by $n, C_n$. Total variation denoising, also known as the fused lasso, is seen to be rate optimal. Several simpler estimators exist, such as Laplacian smoothing and Laplacian eigenmaps. A natural question is: can these simpler estimators perform just as well?

This story appears in the April 2026 print edition. While some stories from this issue are not yet available to read online, you can explore more from the magazine . Get our editors' guide to what matters in the world, delivered to your inbox every weekday. The race to power AI is already remaking the physical world. Three Mile Island's cooling towers have until recently served as grave markers for America's nuclear-power industry. A s we drove through southwest Memphis, KeShaun Pearson told me to keep my window down--our destination was best tasted, not viewed. Along the way, we passed an abandoned coal plant to our right, then an active power plant to our left, equipped with enormous natural-gas turbines. Pearson, who directs the nonprofit Memphis Community Against Pollution, was bringing me to his hometown's latest industrial megaproject.

Implicit Neural Representations (INRs) have previously been used to represent and compress image and video content, demonstrating relatively high decoding speed compared to other methods.

Though LLMs are capable of generating plausible programs, it's challenging to interact with the LLMs further to revise the program, especially if the user's specific requirements are different from the initial proposal.