Acta Numerica 2021: Volume 30 Acta Numerica Series

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.

1. Numerical homogenization beyond scale separation Robert Altmann, Patrick Henning and Daniel Peterseim; 2. Deep learning: a statistical viewpoint Peter L. Bartlett, Andrea Montanari and Alexander Rakhlin; 3. Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation Mikhail Belkin; 4. Optimal transportation, modelling and numerical simulation Jean-David Benamou; 5. Neural network approximation Ronald DeVore, Boris Hanin and Guergana Petrova; 6. Learning physics-based models from data: perspectives from inverse problems and model reduction Omar Ghattas and Karen Willcox; 7. Tensors in computations Lek-Heng Lim; 8. Modelling and computation of liquid crystals Wei Wang, Lei Zhang and Pingwen Zhang.

Arieh Iserles is Emeritus Professor of Numerical Analysis of Differential Equations at the University of Cambridge.
Douglas Arnold is McKnight Presidential Professor of Mathematics at the University of Minnesota.