Aims. The identification of active galactic nuclei (AGNs) is extremely important for understanding galaxy evolution and its connection with the assembly of supermassive black holes (SMBHs). With the advent of deep- and high-angular-resolution imaging surveys such as those conducted with the James Webb Space Telescope (JWST), it is now possible to identify galaxies with a central point source out to the very early Universe. In this proof of concept study, we aim to develop a fast, accurate, and precise method of identifying galaxies that host AGNs and recover the intrinsic AGN contribution fraction (fAGN). Methods. We trained a deep learning (DL) -based method, Zoobot, to estimate the fractional contribution of a central point source to the total light. Our training sample comprises realistic mock JWST images of simulated galaxies from the IllustrisTNG cosmological hydrodynamical simulations. We injected different amounts of the observed JWST point spread functions to represent galaxies with varying levels of AGN contributions. Galaxies in our training sample span a wide range of morphologies, including mergers. We analysed in detail the performance of our method as a function of various galaxy properties and compared it with results obtained from the traditional light profile fitting tool GALFIT. After training, we applied our method to real JWST observations in the COSMOS field. Results. We find an excellent performance of our DL method in recovering the injected fAGN, in terms of precision and accuracy. The mean difference between the predicted and true fAGN is −0.002 and the overall root mean squared error (RMSE) is 0.013. The overall relative absolute error (RAE) is 0.076, and the outlier (defined as predictions with RAE > 20%) fraction is 6.5%. In comparison, using GALFIT, we achieve a mean difference of ─0.02, a RMSE of 0.12, a RAE of 0.19, and an outlier fraction of 19%. We also investigate how these key performance metrics obtained from Zoobot and GALFIT vary as a function of the injected fAGN, redshift, signal-to-noise ratio, and galaxy size. In addition to the superior performance, our DL method has several other advantages over traditional methods. For example, it has a much higher success rate (even for highly disturbed or irregular galaxies) and is extremely fast. We applied our trained DL model to real JWST observations and found that 20% of the X-ray-selected AGNs and 8% of the MIR-selected AGNs are also identified as AGNs using a cut at fAGN > 0.2. When using fAGN > 0.1, these overlaps increase to 33% for the X-ray AGNs and 15% for the MIR AGNs. In summary, our DL-based method of identifying AGNs and estimating the AGN contribution fraction has a huge potential in future applications to large galaxy imaging surveys.
