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+ - navigation
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+<!DOCTYPE html>
+#
+<html lang="en">
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+  <meta charset="utf-8">
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+<body>
+  <p>
+  <i class="footer">This page was last updated on 2024-05-21 05:05:49 UTC</i>
+  </p>
+
+  <div class="note info" onclick="startIntro()">
+    <p>
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+        Click here for a quick intro of the page! <i class="material-icons">help</i>
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+  <p>
+  <h3 data-intro='Recommendations for the article'>
+    Recommendations for the article <i>Rediscovering orbital mechanics with machine learning</i>
+  </h3>
+  <table id="table1" class="display wrap" style="width:100%">
+  <thead>
+    <tr>
+        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
+        <th>Title</th>
+        <th>Authors</th>
+        <th>Publication Date</th>
+        <th>Journal/ Conference</th>
+        <th>Citation count</th>
+        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
+    </tr>
+  </thead>
+  <tbody>
+
+        <tr id="We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/a6aad9ccdcb7674a3b7ab710f0a80d205834f847" target='_blank'>Learning Symbolic Physics with Graph Networks</a></td>
+          <td>
+            M. Cranmer, Rui Xu, P. Battaglia, S. Ho
+          </td>
+          <td>2019-09-12</td>
+          <td>ArXiv</td>
+          <td>73</td>
+          <td>68</td>
+        </tr>
+
+        <tr id="None">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/e87f78aebc1966defb271e39d09f5f0939c79e05" target='_blank'>Celestial Machine Learning - From Data to Mars and Beyond with AI Feynman</a></td>
+          <td>
+            Zi-Yu Khoo, A. Yang, J. Low, S. Bressan
+          </td>
+          <td>2023-12-15</td>
+          <td>ArXiv</td>
+          <td>1</td>
+          <td>31</td>
+        </tr>
+
+        <tr id="None">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/f97840db878f0eff149e999a73c52afc15fb44e3" target='_blank'>Celestial Machine Learning - Discovering the Planarity, Heliocentricity, and Orbital Equation of Mars with AI Feynman</a></td>
+          <td>
+            Zi-Yu Khoo, Gokul Rajiv, Abel Yang, Jonathan Sze Choong Low, Stéphane Bressan
+          </td>
+          <td>2023-12-19</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>3</td>
+        </tr>
+
+        <tr id="We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions, and breakdown timescales for approximate conservation laws.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/f3cf4756b2375cd6694267370a8d98543e781169" target='_blank'>Machine Learning Conservation Laws from Trajectories.</a></td>
+          <td>
+            Ziming Liu, Max Tegmark
+          </td>
+          <td>2021-05-06</td>
+          <td>Physical review letters</td>
+          <td>74</td>
+          <td>81</td>
+        </tr>
+
+        <tr id="Most problems in Earth sciences aim to do inferences about the system, where accurate predictions are just a tiny part of the whole problem. Inferences mean understanding variables relations, deriving models that are physically interpretable, that are simple parsimonious, and mathematically tractable. Machine learning models alone are excellent approximators, but very often do not respect the most elementary laws of physics, like mass or energy conservation, so consistency and confidence are compromised. In this paper, we describe the main challenges ahead in the field, and introduce several ways to live in the Physics and machine learning interplay: to encode differential equations from data, constrain data-driven models with physics-priors and dependence constraints, improve parameterizations, emulate physical models, and blend data-driven and process-based models. This is a collective long-term AI agenda towards developing and applying algorithms capable of discovering knowledge in the Earth system.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/5edea84373b72e73a29b0348e388b4d458664dbd" target='_blank'>Living in the Physics and Machine Learning Interplay for Earth Observation</a></td>
+          <td>
+            Gustau Camps-Valls, D. Svendsen, Jordi Cort'es-Andr'es, 'Alvaro Moreno-Mart'inez, Adri'an P'erez-Suay, J. Adsuara, I. Mart'in, M. Piles, Jordi Munoz-Mar'i, Luca Martino
+          </td>
+          <td>2020-10-18</td>
+          <td>ArXiv</td>
+          <td>5</td>
+          <td>77</td>
+        </tr>
+
+        <tr id="We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/643ac3ef063c77eb02a3d52637c11fe028bfae28" target='_blank'>Discovering Symbolic Models from Deep Learning with Inductive Biases</a></td>
+          <td>
+            M. Cranmer, Alvaro Sanchez-Gonzalez, P. Battaglia, Rui Xu, Kyle Cranmer, D. Spergel, S. Ho
+          </td>
+          <td>2020-06-19</td>
+          <td>ArXiv</td>
+          <td>365</td>
+          <td>105</td>
+        </tr>
+
+        <tr id="The Observation--Hypothesis--Prediction--Experimentation loop paradigm for scientific research has been practiced by researchers for years towards scientific discoveries. However, with data explosion in both mega-scale and milli-scale scientific research, it has been sometimes very difficult to manually analyze the data and propose new hypotheses to drive the cycle for scientific discovery. In this paper, we discuss the role of Explainable AI in scientific discovery process by demonstrating an Explainable AI-based paradigm for science discovery. The key is to use Explainable AI to help derive data or model interpretations, hypotheses, as well as scientific discoveries or insights. We show how computational and data-intensive methodology -- together with experimental and theoretical methodology -- can be seamlessly integrated for scientific research. To demonstrate the AI-based science discovery process, and to pay our respect to some of the greatest minds in human history, we show how Kepler's laws of planetary motion and Newton's law of universal gravitation can be rediscovered by (Explainable) AI based on Tycho Brahe's astronomical observation data, whose works were leading the scientific revolution in the 16-17th century. This work also highlights the important role of Explainable AI (as compared to Blackbox AI) in science discovery to help humans prevent or better prepare for the possible technological singularity that may happen in the future, since science is not only about the know how, but also the know why. Presentation of the work is available at https://slideslive.com/38986142/from-kepler-to-newton-explainable-ai-for-science-discovery.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/2b1143fbed61617fcc27633dd9452a627edb5c99" target='_blank'>From Kepler to Newton: Explainable AI for Science Discovery</a></td>
+          <td>
+            Zelong Li, Jianchao Ji, Yongfeng Zhang
+          </td>
+          <td>2021-11-24</td>
+          <td>ArXiv</td>
+          <td>12</td>
+          <td>9</td>
+        </tr>
+
+  </tbody>
+  <tfoot>
+    <tr>
+        <th>Abstract</th>
+        <th>Title</th>
+        <th>Authors</th>
+        <th>Publication Date</th>
+        <th>Journal/Conference</th>
+        <th>Citation count</th>
+        <th>Highest h-index</th>
+    </tr>
+  </tfoot>
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