Physical Sciences and Mathematics Commons^™

New Physics In The Age Of Precision Cosmology, Vivian I. Sabla

Dartmouth College Ph.D Dissertations

The Lambda-cold dark matter (LCDM) model has become the standard model of cosmology because of its ability to reproduce a vast array of cosmological observations, from the earliest moments of our Universe, to the current period of accelerated expansion, which it does with great accuracy. However, the success of this model only distracts from its inherent flaws and ambiguities. LCDM is purely phenomenological, providing no physical explanation for the nature of dark matter, responsible for the formation and evolution of large-scale structure, and giving an inconclusive explanation for dark energy, which drives the current period of accelerated expansion.

Furthermore, cracks …

Symplectically Integrated Symbolic Regression Of Hamiltonian Dynamical Systems, Daniel Dipietro

Computer Science Senior Theses

Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTMRNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integration scheme; prediction performance is used to train the LSTM-RNN to generate increasingly better functions via a risk-seeking policy gradients …