The inverse problem seeks for the source given a response. It has always been an important step in numerically addressing many physical problems and in forming optimal solutions towards practical applications. However, it is a notoriously difficult problem to solve as the kernel functional is usually ill-behaviored to be accurately inverted. A better solution towards inverse models will benefit our society by lending new insights and introducing more efficient solutions to realistic world of both scientific and technical interests. This symposium focuses on a specific aspect of the cross-disciplinary inverse problem with an emphasis on the development and application of new methods towards physical science research and engineering. It aims at bringing together scholars across the world who are from different fields yet share the joint interest on tackling the inverse problem. It strives to provide a chance to exchange newest ideas and thoughts among researchers on a broad range of problems.