level: research
scientists often want to learn physical laws directly from data. current methods usually work with one dataset at a time. this can be a problem when the data is limited or noisy. in real life, the same physical system may produce many datasets. these datasets differ only in starting conditions or boundary setups. using all of them together could lead to better equation discovery.
a new framework called mco-pde tackles this by using multiple data sources. it first builds separate neural network models for each dataset. then it uses a soft-competitive weighting system. this system checks how reliable each dataset is and combines them into one agreed-upon equation coefficient. a genetic algorithm searches for the best equation structure at the same time. this means the method finds both the form of the equation and its parameters together.
the approach was tested on several partial differential equations. it outperformed single-dataset methods, especially when individual datasets were small or incomplete. the weighting mechanism automatically downplayed bad data. this made the final equation more accurate. the method does not need prior knowledge about which dataset is best. it learns that during the process. this could help in fields like fluid dynamics or climate modeling where multiple experiments exist.
why it matters: it lets researchers extract reliable physical laws from multiple imperfect datasets, improving model accuracy when data is scarce or noisy.