Traditional cosmological analyses rely on compressing observational data into summary statistics — most commonly the two-point correlation function or power spectrum. While this approach is optimal for Gaussian random fields, the nonlinear gravitational evolution of cosmic structure introduces significant non-Gaussianity on small scales. This means that summary statistics inevitably discard cosmological information, particularly about parameters like the neutrino mass and the equation of state of dark energy that leave their strongest signatures in the nonlinear regime. My work develops methods that go beyond these limitations to optimally and robustly extract cosmological information.

Field-Level BAO Reconstruction

Baryon acoustic oscillations (BAO) are one of the most powerful probes in cosmology — a standard ruler imprinted in the distribution of matter by sound waves in the early Universe. Measuring the BAO scale with high precision is critical for constraining the expansion history of the Universe and the nature of dark energy. I have developed field-level inference methods for BAO reconstruction, first reconstructing the initial linear density field and then fitting the BAO signal therein. By benchmarking traditional reconstruction against explicit field-level inference using differentiable forward modeling with hybrid effective field theory, as well as implicit field-level inference using convolutional neural networks, we show that field-level approaches significantly sharpen the BAO feature relative to traditional reconstruction on DESI-like galaxy catalogs. This is an exciting result because it demonstrates that field-level methods can meaningfully improve constraints on the expansion history of the Universe from existing and upcoming surveys.

Field-Level Inference

Instead of compressing the data, field-level inference performs inference directly on the full three-dimensional matter field. By forward-modeling the evolution of the Universe from initial conditions to the observed field and comparing the result to data, we can in principle extract all of the available cosmological information — not just the fraction captured by summary statistics.

Sampling the posterior distribution over initial conditions of the Universe is an extraordinarily high-dimensional problem — the number of parameters equals the number of voxels in the volume being analyzed, often in the millions. I have worked on applying Microcanonical Langevin Monte Carlo (MCLMC) to this problem. MCLMC is a gradient-based sampling algorithm that is particularly well-suited to high-dimensional spaces, achieving over an order of magnitude greater efficiency than traditional Hamiltonian Monte Carlo. This enables efficient exploration of the posterior over initial conditions and, in turn, tight constraints on cosmological parameters from the full field.

Robustness of Field-Level Inference

Extracting maximal information from cosmological data is only meaningful if the results are robust. A critical question is whether the simulations used to train or calibrate inference pipelines introduce systematic biases. I have conducted the first field-level comparison and robustness analysis of cosmological N-body simulations, evaluating widely used codes including Abacus, Gadget, and others. We find that differences between simulation codes — particularly between adaptive mesh refinement (AMR) and non-AMR methods — can introduce biases larger than those from hydrodynamic effects, and that even resolution differences within the same code lead to biased inference. These findings motivate the need for careful data filtering and the use of field-level out-of-distribution metrics to ensure robust cosmological constraints.

Simulation-Based Inference

A key challenge is that the likelihood of the full field is intractable — we cannot write down an analytic expression for the probability of observing a given configuration of galaxies. Simulation-based inference (SBI) circumvents this by using simulations as an implicit likelihood. Rather than evaluating the likelihood directly, SBI methods learn the mapping from simulated data to posterior distributions over cosmological parameters using neural networks. I have contributed to developing SBI benchmarks for upcoming surveys like LSST, establishing the accuracy and reliability of these methods for real-world cosmological analysis. I have also applied SBI to robust CMB B-mode analysis, combining needlet internal linear combination (NILC) with simulation-based inference to perform a complete maps-to-parameters analysis of large-scale CMB polarization. Trained on a relatively simple foreground model, the method yields unbiased results across a range of complex Galactic foreground simulations, demonstrating the feasibility of SBI for current ground-based CMB observatories.

Neural Networks for Neutrino Mass

Standard analyses compress the rich information in weak lensing maps into the power spectrum. However, in the nonlinear regime, significant information is encoded in the higher-order structure of the fields. I have developed convolutional neural network (CNN) architectures that operate directly on weak lensing convergence maps to constrain the neutrino mass. By learning to extract non-Gaussian features that are invisible to two-point statistics, these networks can substantially tighten neutrino mass constraints beyond what is achievable with traditional methods.

Interpretability

As machine learning methods become central to cosmological inference, understanding what the networks actually learn is essential for building trust in their predictions. I have worked on interpreting the field-level neutrino mass information extracted by CNNs from weak lensing convergence maps, identifying the scales, redshifts, and density regimes from which the networks draw their constraining power. Complementing this, I have also investigated how CNNs extract cosmological information from the matter density field in the presence of complex baryonic processes, identifying the Fourier scales, density scales, and morphological features of the cosmic web that the networks pay most attention to. Overdense regions provide the most information per pixel, while underdense regions — particularly deep voids — contribute significantly due to their large spatial extent and coherent features.

Transfer Learning

Training neural networks for cosmological inference typically requires large numbers of expensive simulations for each cosmological model. Transfer learning offers a way to dramatically reduce this cost. I have shown that pre-training on the standard ΛCDM model and fine-tuning on beyond-ΛCDM scenarios — including massive neutrinos, modified gravity, and primordial non-Gaussianities — can enable inference with significantly fewer simulations, though negative transfer can occur when strong physical degeneracies exist. I have also developed multi-fidelity SBI methods that combine simulation sets of varying fidelity using feature matching and knowledge distillation, resulting in improved posterior quality particularly for small simulation budgets.

Velocity Reconstruction

Galaxy peculiar velocities contain a wealth of cosmological information that is complementary to galaxy positions alone. I have developed methods for joint velocity and density reconstruction, combining galaxy clustering and peculiar velocity data to tighten constraints on cosmological parameters. Peculiar velocities are particularly powerful for breaking degeneracies between parameters like the growth rate of structure and the amplitude of matter fluctuations.

These methods — field-level inference, simulation-based inference, machine learning, and multi-probe reconstruction — represent the frontier of cosmological data analysis and are critical for fully exploiting the enormous datasets arriving from the next generation of surveys.