Earlier quoted context omitted.
Ansys, Abaqus CAE, Dyna, Optistruct, FEKO, AcuSolve, NASTRAN, ... The list goes on and on. Each bigger DE or partial DE has a huge ecosystem of numerical software around it to approximate solutions for real world applications. High and low electro magnetics (Maxwell), Navir-Stokes, ...
What tools are used for parameter estimation? E.g. I made a model that describes my system behavior, then collected a lot of data and next need to find the constants in the model that make the best fit. Thank you.
The search terms there would be "Model Calibration" and/or "System Identification" Software.
I think those are again very domain specific. But there are a few.
PS: While AI and machine learning are catching on in many different fields, the software packages in those domains make heavy use of fairly complicated fitting and approximations methods already. Lots or correlation and effect estimation, which builds many of the underlying guts of machine learning.