Advanced Analytics on Smart Data

The objectives of ANALYST have been to develop new methods for the analysis of large datasets with a spatial structure. The datasets in focus have millions to hundreds of millions of points. The research has, in cooperation with Norwegian Hydrographic Service addressed sea bottom and terrain data collected by Lidar and sonar, and in cooperation with the Intervention Centre at Oslo University Hospital addressed layered medical data from CT and MR scans. These data types have in common an underlying piecewise smooth structure. The hypothesis has been that: 1. Such datasets can be accurately represented mathematically by spline technology; 2. That the locally refined splines developed by SINTEF in the last decade (LR B-splines) are especially suited for compact representation of datasets with large local variations. It has also been important to focus on how artificial intelligence complements traditional spline algorithms, both regarding performance and the ability to address new challenges. Sea bottom and terrain datasets can both have different sorts of spatial structures. There are digital terrain and surface models with regular structures, and there can be nonregular structured data from Lidar and sonar. For data with a regular structure neural networks have been modified to fill in holes with credible values in cooperation with a visiting PhD-fellow from the ARCADES Marie-Curie network. For processing of nonregular data the development of new neural network has started in ANALYST and is now continued by a SINTEF employed PhD-fellow in the GRAPES Marie-Curie network. For the nonregular datasets the methods developed are based on LR B-splines with no use of neural networks. During the last two years the activity targeting sea bottom and terrain data has also, in cooperation with the University of Hannover, addressed how to control the LR B-spline approximation by information models. The approximation starts by approximation a compact smooth surface to the dataset. Then new degrees of freedom (approximation power) are gradually added in areas where the surface has the largest approximation error. Information models makes it possible to stop the process when added new degrees of freedom contribute little to the overall accuracy. We have also, with success, address how existing algorithms targeting Computer Aided Design can be used for relevant analysis of the generated models. Detection of changes over time by comparing measurements performed in the same area has also been central. A challenge is that datasets from different points in time has different extents and patterns. This makes direct comparison of the datasets difficult. We have found it much simpler to compare surfaces that represents different points in time, or points from one point in time with a surface representing another point in time. Vi have further added a time axis to the datasets and approximated the space-time volume with an LR B-spline volume. Both approaches provide a good basis for change detection. Tensor product spline representation and neural networks have been combined with success for layered medical data. In a tensor product surface, the coefficients are organized in a regular grid, like the organization of pixels in an image. Neural networks employing tensor product splines can, as neural networks for images, efficiently exploit the computational power of GPUs. Even though the starting point was CT- and MR-scans, the developed methods are well suited for other types of layer sensor data, e.g., from Additive Manufacturing (3D Printing). Expected impacts from ANALYST are: - Within spline research LR B-splines are very promising with respect to compact representation and processing of large datasets with a piecewise smooth structure in two or more variables. It has also been shown that among the alternative locally refined spline methods LR B-splines is the most flexible. - It has been demonstrated that neural networks can directly generate spline coefficients and thereby code the results in a significantly more compact way that pixels and voxels. - A bridge has been created between spline and neural network research that shows that combining knowledge from both research fields open new doors. - For business, industry, and society it is demonstrated for scattered sea bottom data that compact ocean floor models with guaranteed quality can be created. These are very well suited of mathematical type analysis. - For layered medical data spline representations can be created that are well suited for mathematical analysis and significantly more compact that voxel representations. - An overall benefit is the possibility to create digital twins from sensor data for a wide range of applications. Twins that can efficiently be analysed and comparted with existing or future information and data.

- Kartverkets sjødivisjon sendte i november 2021 inn en søknad til Kommunal- og distriktsdepartementet om finansiering av en ny satsing på "Marine grunnkart i kystsonen". Her er resultater fra ANALYST er en svært aktuell teknologi. - For lagvise (medisinske) data kan en direkte skape spline representasjoner som er svært godt egnet for matematisk analyse og betydelig mer kompakte en voxel representasjon. - En overordnet nytteverdi er muligheten til å skape digitale tvillinger fra sensordata for et bredt spekter av anvendelser. -SINTEF arbeider med å en "Mission Pilot" innen klimatilpassing i samarbeid med Innlandet fylke der resultater fra ANALYST inngår blant basisteknologier denne kan benytte. - Det er dannet en bro mellom forskning innen spline teknologi og nevrale nettverk som viser at kombinasjon av kunnskap fra begge fagfelter gir nye muligheter. I Marie-Curie nettverket GRAPES videreføres arbeid med de implisitte og spline-baserte nevrale nettverk.

Over the last ten years, a new field of research has emerged: Big Data Analytics (BDA). Massively distributed systems offer new tools for exploring large datasets. In parallel, a steady increase in computing power and available training data has enabled the field of Artificial Intelligence (AI) to gain critical mass. The challenge of managing, investigating, and visualizing big datasets is not new in the fields of Science, Technology, Engineering and Mathematics (STEM). Recent developments in BDA offer a new set of tools for overcoming these challenges, however, there are significant challenges that arise from the structural differences between most STEM data and the unstructured textual data typical in classical Big Data applications. In order to address these challenges, we propose using Locally Refined (LR-) spline data modelling to turn Big Data into Smart Data. In early implementations of LR-spline algorithms in 2D and 3D, we have seen their potential as compact interactive models for visual and quantitative analytics on big datasets, well suited for hardware-accelerated interrogation and visualization. By spatial tiling and stitching, we have an extremely versatile and parallelizable approach, well suited for Big Data infrastructures. We can therefore include time and other relevant variables in a compact, interactive, multi-scale, higher order, locally refined model. However, substantial theoretical developments are needed before this vision of LR-spline modelling of Big Data can be realized. ANALYST will provide the research platform to bring the theoretical foundation of LR-splines up to a level where their full potential can be explored, combining BDA and AI to provide advanced analytics on the LR-spline model. While the focus will be on data from applications in the STEM fields, the resulting algorithms have a wider applicability, providing highly scalable complex modelling tools for Big Data Analytics.