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      "statement": "# Lagrangian neural networks using differentiated Euler–Lagrange dynamics\n\nParameterizes a Lagrangian with a neural network and uses automatic derivatives and a velocity-Hessian inverse to predict accelerations from generalized coordinates.\n\n## Scientific scope\n\nSix original authors; affiliation stars are not shared-lead marks. Inherits Euler–Lagrange mechanics and earlier restricted DeLaN; not first neural Lagrangian method. Invertibility/regularity are needed for unambiguous dynamics; pseudoinverse is a practical response to singularity, not proof of a regular physical system. Cubic Hessian inversion and integration error remain; learned conservation is not universal true-energy accuracy.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nMiles Cranmer; Sam Greydanus; Stephan Hoyer; Peter Battaglia; David Spergel; Shirley Ho\n\nSource-listed authors or explicitly credited technical contributors for the cited versions. Family entries retain source-specific attribution; a combined list is not one original-paper byline or equal individual work. Names alone do not establish resolved identities.\n\n\n\n## Original sources\n\n- [Lagrangian Neural Networks](https://arxiv.org/pdf/2003.04630v1)\n",
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