DEMNet: Evaluating Solar Differential Emission Measure Inversion with Deep Learning

V. Samuel Pérez-Díaz¹, Ruoyu Wang¹, Karin Dissauer^2,3, KD Leka², David Fouhey¹

¹ Courant Institute, New York University ² NorthWest Research Associates ³ University of Graz

DEMNet vs Basis Pursuit across log-temperature bins during the 2017 Sep. 10 X8.2 flare — (Top) The six SDO/AIA EUV input channels, each sensitive to plasma at a different coronal temperature. (Bottom) DEMNet vs. classical Basis Pursuit across temperature bins during the 2017 Sep. 10 X8.2 solar flare. Green pixels mark Basis Pursuit failures.

Abstract

The Differential Emission Measure (DEM) is a key diagnostic tool for understanding the solar atmosphere; commonly it connects images obtained in the extreme ultraviolet to the thermal structure of the solar corona through mathematical inversion. Traditional DEM inversion methods are based on per-pixel optimization and are very computationally expensive, thus prohibitive for large-scale analysis.

We present and analyze DEMNet, a deep learning model that emulates a classical solver. DEMNet is far faster, provides uncertainties, and is smoother over multiple dimensions than traditional methods. We analyze DEMNet's predictions as well as several design decisions that are critical to its success.

CV4Science @ CVPR 2026 Physics and AI Conference (PAI26) @ Stanford Paper (coming soon)

Performance at a Glance

DEMNet Basis Pursuit

Inference speed 2.85M px/s ~1.5K px/s/core

Resynthesis error 12.2% 28.3%

What the Network Learned

A critical question when deploying a neural network in a scientific pipeline is: what did it actually learn? We probe this through two lenses: structure and scale.

To understand the learned structure, we compare DEMNet to a K-nearest-neighbor (KNN) model built on the full training set. For most pixels, the two methods agree closely, suggesting the network behaves largely as a smooth lookup table over AIA input space. The divergence happens at high intensities, exactly where the physics is most interesting: there, DEMNet's learned non-linearity gives it an advantage.

KNN vs DEMNet comparison — **KNN vs. DEMNet.** (Left) Joint density of errors in log scale; the diagonal indicates near-identical performance for most pixels. (Center) Same density colored by AIA 193 intensity ; divergence concentrates at the brightest regions. (Right) Per-pixel MSE difference during the 2017 Sep. 10 flare ; red: DEMNet outperforms KNN; blue: reverse. The pre-flare loop is the key region where DEMNet has an edge.

**KNN vs. DEMNet.** (Left) Joint density of errors in log scale; the diagonal indicates near-identical performance for most pixels. (Center) Same density colored by AIA 193 intensity ; divergence concentrates at the brightest regions. (Right) Per-pixel MSE difference during the 2017 Sep. 10 flare ; red: DEMNet outperforms KNN; blue: reverse. The pre-flare loop is the key region where DEMNet has an edge.

The scaling plot reveals that performance improves consistently with more data. Bright pixels (active regions, flares, coronal loops) are the hardest cases and benefit the most from scale. Quiet-sun pixels, which make up the bulk of the disk, are largely saturated even at smaller training sizes, consistent with the KNN finding that these can be retrieved by possibly a simpler model. Forward-model finetuning (star) further improves resynthesis at a modest accuracy cost.

DEMNet

colorbar — **Temporal snapshots** during the 2017 Sep. 10 X8.2 flare. Time series (bottom) for a single pixel from DEMNet and Basis Pursuit; red regions mark Basis Pursuit failures. log-transformed.

DEMNet is a pixel-wise neural network that maps six EUV filter observations from NASA's SDO/AIA (at 94, 131, 171, 193, 211, 335 Å) to the DEM vector over 18 temperature bins. It builds on the earlier DeepEM model, adding Fourier frequency encodings to capture sharp intensity variations, uncertainty quantification via a classification head, and a physics-inspired forward-model finetuning stage. The model is trained on ~293K patches from 917 full-disk timestamps (Jan 2014 – Dec 2015), using inversions from classical methods as targets.

DEMNet processes pixels independently and produces outputs that are smooth both across space and over time. The figure on the right shows four frames during the impulsive phase of the 2017 Sep. 10 X8.2 flare: DEMNet predicts the evolution of the event smoothly. The time series highlights the failures of Basis Pursuit (red region), where DEMNet continues to produce plausible predictions throughout.