Computing Nonlinear Power Spectra Across Dynamical Dark Energy Model Space with Neural ODEs

I show how to compute the nonlinear power spectrum across the entire <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> dynamical dark energy model space. Using synthetic ΛCDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear matter power spectrum as a function of the background expansion and mean matter density across ∼9 Gyr of cosmic evolution. After training, the model generalises to &lt;em&gt;any&lt;/em&gt; dynamical dark energy model parameterised by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>w</mml:mi> <mml:mrow> <mml:mo stretchy="true" form="prefix">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="true" form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . With little optimisation, the neural ODE is accurate to within 4% up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> <mml:mspace width="0.167em"/> <mml:mi>h</mml:mi> <mml:mspace width="0.167em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> <mml:mi>p</mml:mi> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.