Learning Integrable Dynamics with Action-Angle Networks

Machine learning has become increasingly popular for efficiently modelling the dynamics of complex physical systems, demonstrating a capability to learn effective models for dynamics which ignore redundant degrees of freedom. Learned simulators typically predict the evolution of the system in a step-by-step manner with numerical integration techniques. However, such models often suffer from instability over long roll-outs due to the accumulation of both estimation and integration error at each prediction step. Here, we propose an alternative construction for learned physical simulators that are inspired by the concept of action-angle coordinates from classical mechanics for describing integrable systems. We propose Action-Angle Networks, which learn a nonlinear transformation from input coordinates to the action-angle space, where evolution of the system is linear. Unlike traditional learned simulators, Action-Angle Networks do not employ any higher-order numerical integration methods, making them extremely efficient at modelling the dynamics of integrable physical systems.Comment: Accepted at Machine Learning and the Physical Sciences workshop at NeurIPS 202

Privacy-Utility Trade-offs in Neural Networks for Medical Population Graphs: Insights from Differential Privacy and Graph Structure

We initiate an empirical investigation into differentially private graph neural networks on population graphs from the medical domain by examining privacy-utility trade-offs at different privacy levels on both real-world and synthetic datasets and performing auditing through membership inference attacks. Our findings highlight the potential and the challenges of this specific DP application area. Moreover, we find evidence that the underlying graph structure constitutes a potential factor for larger performance gaps by showing a correlation between the degree of graph homophily and the accuracy of the trained model

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science

Magnetic Field Boundaries in Cassini Plasma Spectrometer Data

This dataset consists of: get_files.sh - a bash script to download ELS data (.DAT and .LBL) files. crossing_events_urls.txt - a text file containing URLs for each of the ELS data files. get_files.sh reads this file directly. crossing_events.txt - a text file containing the list of crossing events with associated data, obtained by processing Table S1 in [1]. labels.zip - a zip file containing directory with events for each DAT file, in YAML format. plotter.py - a plotting script in Python. requirements.txt - a file indicating dependencies for the plotting script. Data This dataset spans 1259 observations from CAPS ELS, each with a .LBL file and a .DAT file. Together, these take 128 GB of space. To download these files, do: ./get_files.sh in a Bash shell/terminal. The files are stored in the &#39;data/&#39; folder (created if not present) in the current directory. ELS data files are obtained from NASA&#39;s Planetary Data System at https://pds-ppi.igpp.ucla.edu/search/view/?f=yes&amp;amp;id=pds://PPI/CO-E_J_S_SW-CAPS-3-CALIBRATED-V1.0/DATA/CALIBRATED For help in understanding the ELS data files, see the CAPS User Guide at https://pds-ppi.igpp.ucla.edu/ditdos/download?id=pds://PPI/COCAPS_1SAT/DOCUMENT/CAPS_USER_GUIDE/CAPS_PDS_USER_GUIDE_V1_00.PDF. Labels Unzipping the labels.zip file will create a labels/ folder in the current directory, requiring 28MB of space. Within labels/: bs/ - includes bow shock crossing events. mp/ - includes magnetopause crossing events. dg/ - includes known data-gap events. See [1]. sc/ - includes unreliable data events. See [1]. valid/ - union of all files in bs/ and mp/. all/ - union of all files in bs/, mp/, dg/ and sc/. Within the labels/bs/ and labels/mp/ folders: in/ - crossing events with the transition direction as inward. out/ - crossing events with the transition direction as outward. all/ - union of all files in in/ and out/. Each label file is a YAML file containing a &#39;change_points&#39; field. The entries under this field each indicate the time of a transition event. The other fields (&#39;bimodality&#39; and &#39;negative_ions&#39;) are not relevant for this dataset. Plotting the Data (and Labels) To help visualize the data and labels, we supply a plotting script plotter.py, in Python (version 2.7). First, install dependencies with: pip install -r requirements.txt and then run: ./plotter.py -h to see the available options. Example usage (after downloading data and unzipping labels): ./plotter.py data/ELS_200418018_V01.DAT -l labels/mp/all/ELS_200418018_V01.yaml --interpolated -f max_filter -fsize 100 --title &quot;An Observation from CAPS ELS&quot; will open up a new window with a plot of the data. To directly save to a file, use the &#39;-o savefilename&#39; option. For example, ./plotter.py data/ELS_200418018_V01.DAT -l labels/mp/all/ELS_200418018_V01.yaml --interpolated -f max_filter -fsize 100 --title &quot;An Observation from CAPS ELS&quot; -o ELS_200418018_V01.png References [1] Jackman, C. M., Thomsen, M. F., &amp;amp; Dougherty, M. K. (2019). Survey of Saturn&#39;s magnetopause and bow shock positions over the entire Cassini mission: Boundary statistical properties and exploration of associated upstream conditions. Journal of Geophysical Research: Space Physics, 124, 8865&ndash; 8883. https://doi.org/10.1029/2019JA026628 The original table of magnetopause and bow shock crossing events can be found at https://agupubs.onlinelibrary.wiley.com/action/downloadSupplement?doi=10.1029%2F2019JA026628&amp;amp;file=jgra55251-sup-0001-Table_SI-S01.txt Grants NASA Contract through JPL with South West Research Institute. Grant Number: 1243218 Science and Technology Facilities Council. Grant Number: ST/L004399/1 NASA. Grant Number: 1243218 Diamond Jubilee Fellowship STFC. Grant Number: ST/L004399/1</span