For his research in the field of nonlinear partial differential equations, Siddhartha Mishra has received the 2023 Rössler Prize. In addition, ETH Zurich's most highly endowed research prize recognises that Mishra bridges the gap between mathematical fundamentals and their application in research and industry. For example, he has designed robust, efficient algorithms that enable faster and more accurate simulations of nonlinear partial differential equations on supercomputers. These simulations pave new ways to solve real-world problems in research areas such as astrophysics, solar physics, geophysics, climate dynamics, and biology.
Abstract equations for real-world problems
Real-world problems are the be-all and end-all of Siddhartha Mishra's research: “The phenomena I deal with have a real-world impact,” says Mishra, “and understanding the effects of changes is key to understanding physical and engineering processes in the real world.” Typical questions for his research include, “How much does drag decrease when the shape of the wing on an aircraft is changed in a certain way? And how much carbon emissions can be saved by designing the shape to be more aerodynamic?” Characteristic of Mishra is his orientation towards applications. He regularly collaborates with engineering researchers and industry. For example, together with researchers at Empa, he has developed fast algorithms to simulate an additive, industrial manufacturing process for 3D printing. This involves using Mishra's algorithms to position a laser beam in real time so that it mills the desired shape out of a metal block.
“The amazing thing about mathematics is how its abstract equations keep enabling new solutions and highly relevant applications for the economy and society,” says Max Rössler, the donor of the Rössler Prize, who himself studied mathematics at ETH Zurich, did his doctorate on orbit calculations in space travel and taught at the Institute for Operations Research. “Siddhartha Mishra's research impressively demonstrates the incredible applicability of mathematics, as his equations support predictions of weather, earthquakes or tsunamis, for example, or also enable productive applications such as 3D printing with metals in industrial manufacturing.”
Approximations to complex situations
As a rule, the nonlinear partial differential equations that Mishra studies relate to real phenomena that – like clouds, tornadoes or solar storms – are very complex and multidimensional and contain many dependencies, interactions, and uncertainties. These problems are often so complex that simple formulas cannot fully describe them. A solution satisfies an equation if, by inserting concrete values, it produces a true statement consistent with the measured facts.
