The goal of the project is to develop a new mathematical and computational modeling framework for from biomedical data extracted from biomedical experiments such as voltages, spectra (e.g. mass, magnetic resonance, impedance, optical absorption, …), microscopy or radiology images, gene expression, and many others. Scientists who are looking to understand relationships between different molecular and cellular measurements are often faced with questions involving deciphering differences between different cell or organ measurements. Current approaches (e.g. feature engineering and classification, end-to-end neural networks) are often viewed as “black boxes,” given their lack of connection to any biological mechanistic effects. The approach we propose builds from the “ground up” an entirely new modeling framework build based on recently developed invertible transformation. As such, it allows for any machine learning model to be represented in original data space, allowing for not only increased accuracy in prediction, but also direct visualization and interpretation. Preliminary data including drug screening, modeling morphological changes in cancer, cardiac image reconstruction, modeling subcellular organization, and others are discussed.