Comprehensive spatiotemporal modeling and forecasting systems for ocean dynamics necessitate robust and efficient data delivery and visualization techniques. The multidisciplinary simulation, estimation, and assimilation systems group at MIT (MSEAS) focuses on capturing and predicting diverse ocean dynamics, including physics, acoustics, and biology on varied scales, thereby developing new methods for multi-resolution ocean prediction and analysis, including data generation and assimilation. The group has primarily used non-interactive ocean plots to visualize its simulated and measured data. Although these maps and sections allow for analysis of ocean physics and the underlying numerical schemes, more interactive maps provide more user control over depicted data, allowing easier study and pattern identification on multiple scales. Integrating static and geospatial data in dynamic visualization creates a heightened viewpoint for analysis, enhances ocean monitoring and prediction, and contributes to building scientific knowledge. This thesis focuses on explaining the motivation behind and the methodologies applied in designing these interactive maps.

We combine decision theory with fundamental stochastic time-optimal path planning to develop partial-differential-equations-based schemes for risk-optimal path planning in uncertain, strong and dynamic flows. The path planning proceeds in three steps: (i) predict the probability distribution of environmental flows, (ii) compute the distribution of exact time-optimal paths for the above flow distribution by solving stochastic dynamically orthogonal level set equations, and (iii) compute the risk of being suboptimal given the uncertain time-optimal path predictions and determine the plan that minimizes the risk. We showcase our theory and schemes by planning risk-optimal paths of unmanned and/or autonomous vehicles in illustrative idealized canonical flow scenarios commonly encountered in the coastal oceans and urban environments. The step-by-step procedure for computing the risk-optimal paths is presented and the key properties of the risk-optimal paths are analyzed.

Ocean data assimilation is increasingly recognized as crucial for the accuracy of the real-time ocean prediction systems. Here, the current status of ocean data assimilation in support of the operational demands of analysis and forecasting is reviewed, focusing on the methods currently adopted in operational prediction systems. Significant challenges associated with the most commonly employed approaches are identified and discussed. Overarching issues faced by ocean data assimilation in general are also addressed, and important future directions in response to scientific advances, evolving and forthcoming ocean observing systems and the needs of stakeholders and downstream applications are presented.

Many aspects of geosciences pose novel problems for intelligent systems research. Geoscience data is challenging because it tends to be uncertain, intermittent, sparse, multiresolution, and multiscale. Geosciences processes and objects often have amorphous spatiotemporal boundaries. The lack of ground truth makes model evaluation, testing, and comparison difficult. Overcoming these challenges requires breakthroughs that would significantly transform intelligent systems, while greatly benefitting the geosciences in turn. Although there have been significant and beneficial interactions between the intelligent systems and geosciences communities, the potential for synergistic research in intelligent systems for geosciences is largely untapped. A recently launched Research Coordination Network on Intelligent Systems for Geosciences followed a workshop at the National Science Foundation on this topic. This expanding network builds on the momentum of the NSF EarthCube initiative for geosciences, and is driven by practical problems in Earth, ocean, atmospheric, polar, and geospace sciences. Based on discussions and activities within this network, this article presents a research agenda for intelligent systems inspired by geosciences challenges.

Abstract: A grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviours expressed by differential equations with the vast data sets available in many fields of engineering, science, and technology. At the intersection of probabilistic machine learning, deep learning, and scientific computations, this work is pursuing the overall vision to establish promising new directions for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. To materialize this vision, this work is exploring two complementary directions: (1) designing data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and non-linear differential equations, to extract patterns from high-dimensional data generated from experiments, and (2) designing novel numerical algorithms that can seamlessly blend equations and noisy multi-fidelity data, infer latent quantities of interest (e.g., the solution to a differential equation), and naturally quantify uncertainty in computations. The latter is aligned in spirit with the emerging field of probabilistic numerics.

Biography: Maziar Raissi is currently an Assistant Professor of Applied Mathematics (research) in the Division of Applied Mathematics at Brown University. He received his Ph.D. in Applied Mathematics & Statistics, and Scientific Computations from University of Maryland – College Park in December 2016. His expertise lies at the intersection of Probabilistic Machine Learning, Deep Learning, and Data Driven Scientific Computing. In particular, he has been actively involved in the design of learning machines that leverage the underlying physical laws and/or governing equations to extract patterns from high-dimensional data generated from experiments.