Flawed conservation laws are consequences of a much deeper principle: Noether’s theorem. Conservation laws are among the most important tools in physics. They feel as fundamental as you can get. And ...

We introduce the concept of a weak symmetry group of a system of partial differential equations, that generalizes the "nonclassical" method introduced by Bluman and Cole for finding group-invariant ...

Emmy Noether showed that fundamental physical laws are just a consequence of simple symmetries. A century later, her insights continue to shape physics. In the fall of 1915, the foundations of physics ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...