WEAK LENSING (WL) IS A PROMISING METHOD TO STUDY THE PROPERTIES OF DARK ENERGY TEST DEPARTURES FROM GENERAL RELATIVITY AND MEASURE THE TOTAL MASS OF NEUTRINOS. THE FIRST WL COSMOLOGY EXPERIMENTS HAVE RECENTLY BEEN PERFORMED BOTH IN THE CONTEXT OF GALAXY LENSING (BY CFHTLENS AND DES) AND CMB LENSING (BY ACT SPT AND PLANCK). THESE EXPERIMENTS HAVE PROVIDED INDEPENDENT EVIDENCE FOR DARK ENERGY AND HOLD THE POTENTIAL OF SIGNIFICANTLY TIGHTENING THEIR SENSITIVITY WHILE OFFERING VALUABLE CROSS-CHECKS BETWEEN GALAXY AND CMB LENSING MEASUREMENTS. NON-LINEAR FEATURES WILL BE READILY MEASURABLE IN BOTH GALAXY LENSING AND CMB LENSING DATA AND WILL CONTAIN MORE COSMOLOGICAL INFORMATION THAN AVAILABLE FROM TRADITIONAL GAUSSIAN STATISTICS. THE PROPOSED RESEARCH WILL INVESTIGATE WL IN THE NON-LINEAR REGIME. FORTHCOMING LARGE WL DATASETS WILL HAVE UNPRECEDENTED PRECISION PRESENTING AN EXCITING YET CHALLENGING TASK FOR THE WL COMMUNITY: HOW CAN ONE EXTRACT THE MAXIMUM AMOUNT OF INFORMATION FROM LENSING OBSERVABLES WHILE MINIMIZING THE IMPACT OF SYSTEMATIC ERRORS? THE PROPOSED RESEARCH WILL ANSWER THIS QUESTION BY STUDYING NON-GAUSSIAN STATISTICS WHICH EXTRACT COSMOLOGICAL CONSTRAINTS FROM THE NON-LINEAR REGIME USING A LARGE SUITE OF COSMOLOGICAL RAY-TRACING SIMULATIONS. IN HIS PAST WORK THE PI AND HIS GROUP HAVE DEMONSTRATED THE POWER OF NON-GAUSSIAN STATISTICS WITH SIMULATIONS AND HAVE SUCCESSFULLY APPLIED THE TECHNIQUE TO RECENT OBSERVATIONAL DATA (CFHTLENS). THIS PROPOSAL WILL ADVANCE OUR UNDERSTANDING OF THE PHYSICAL ORIGIN OF THESE CONSTRAINTS THOROUGHLY INVESTIGATE THEORETICAL AND OBSERVATIONAL SYSTEMATICS THAT WILL BECOME RELEVANT IN FUTURE SURVEYS INCLUDING THE NON-LINEAR LENSING DISTORTIONS OF CMB ANISOTROPIES. WE WILL ALSO PROVIDE FUTURE EXPERIMENTS WITH A LENSING EMULATOR THAT CAN BE USED DIRECTLY IN DATA ANALYSIS. THROUGH A COLLABORATION BETWEEN PI HAIMAN (ASTRONOMY) AND CO-I HSU (COMPUTER SCIENCE) WE WILL INCORPORATE NOVEL TECHNIQUES INTO OUR ANALYSIS BORROWING ALGORITHMS FROM THE FIELD OF DATA SCIENCE. A THOROUGH AND SYSTEMATIC INVESTIGATION OF THE UTILITY OF THESE NON-GAUSSIAN FEATURES AS PROPOSED HERE WILL BE NECESSARY FOR WFIRST DES LSST AND OTHER LARGE FORTHCOMING GALAXY LENSING SURVEYS AS WELL AS THE CMB EXPERIMENTS ADVACT AND SPT-3G TO REALIZE THEIR FULL POTENTIAL. THE PROPOSED WORK WILL DIRECTLY SUPPORT NASA'S STRATEGIC PLAN OBJECTIVE 1.6: "DISCOVER HOW THE UNIVERSE WORKS EXPLORE HOW IT BEGAN AND EVOLVED AND SEARCH FOR LIFE ON PLANETS AROUND OTHER STARS.