This is the academic web site of Prof. Eric Mjolsness, Departments of Computer Science and Mathematics, University of California Irvine. Content including papers is accessed by the Papers, Projects, etc. tabs above, some of which are hierarchical. An older site is here.
My main research interest currently (as of 2017) is “Mathematical AI/ML for Multiscale Science”. Here mathematical AI is Artificial Intelligence via high-level symbolic representations (such as computer algebra) of applied mathematical analysis, geometry, algebra, etc.; and ML is mathematical Machine Learning. A central application is to trainable changes of spatiotemporal scale in scientific models, which are very useful for pursuing multiscale science. Multiscale science is in turn motivated by the massive success of scientific reductionism, which operates by relating scientific fields that describe nature at different spatial and temporal scales.
When scientific models go spatial, they often result in dynamically changing forms – “Morphodynamics” – that continually alter the patterns of interaction between many other dynamical variables in a good model. This phenomenon poses a fascinating challenge for mathematical/ computational frameworks that would relate different scales. We have pursued this topic particularly in the area of computational plant science.