Research

Learning from physics and data.

How can we reconstruct a system from partial observations in physically meaningful ways?

A probability distribution over possibilities

An inverse problem begins with observations and asks what is the underlying state that could have produced them. For example, temperature measurements may tell us about the unknown thermal conductivity of a material. Limited or noisy data often admit several explanations, which leads to an ill-posed problem. In this setting, the Bayesian approach is a natural fit as it enables uncertainty quantification over the possible explanations. This approach describes these possibilities through a probability distribution, combining prior knowledge from the physics with a model of the observations.

Much of my work uses information field theory, which poses Bayesian inference as a physical field theory taking inspiration from Feynman’s path integral formulation of quantum physics. This method provides a way to carry out Bayesian inference when the unknown is an entire function or field. Rather than reasoning only about a single fitted function, we work with weighted collections of possible functions.

In my physics-informed formulation, physical laws help define the prior - our beliefs before conditioning on data. A separate observation model describes how measurements relate to the unknown field, and combining these gives a posterior that represents our updated beliefs after observing the data.

01

Many possible functions

A family of illustrative curves representing possible physical fields.

A field may be consistent with many explanations before measurements are available.

02

Physics shapes a prior

The same curves with differing emphasis to represent their relative prior probability.

Physical information gives some functions greater probability, without requiring exact agreement.

03

Observations update belief

Illustrative observations with error bars reweight the candidate curves.

A model of measurement noise changes the relative plausibility of these functions.

04

Prediction with uncertainty

Remaining curves, their weighted mean, and a shaded spread represent the posterior prediction.

The updated ensemble describes a prediction and the uncertainty that remains.

Path integrals express averages over possible functions, weighted by their probability.
01

Bayesian inverse problems · Information field theory

Physical knowledge,
with room for model error.

Physical models provide structure when observations are scarce. Yet their equations often contain approximations, unresolved effects, or unknown parameters. Treating an approximate model as exact can lead to confident but misleading conclusions.

I encode physical knowledge through priors that favor functions with lower physical energy or smaller equation residuals. A model-trust parameter controls how strongly that information constrains the field. Learning this parameter alongside other unknowns can help identify disagreement between the physics and the data.

I also study the mathematical foundations of these constructions: how probability measures on functions are defined, how finite approximations converge, and when a maximum a posteriori estimate is unique.

Related work: physics-informed IFT and Brownian bridge priors.

02

Scientific machine learning · Functional priors

What should a neural
network believe?

A Bayesian neural network places a distribution over its weights. The difficulty is understanding what that distribution implies for the functions the network produces. Even a simple weight prior may encode behavior that is hard to interpret.

I study priors defined through desired behavior in function space. The aim is to bring interpretable functional structure into Bayesian neural networks using connections to Gaussian processes.

Related work: Bayesian neural networks with interpretable priors from Mercer kernels.

Five Brownian motion sample paths starting at zero and fluctuating over time from zero to one. Five Bayesian neural network sample paths drawn using the Mercer prior, showing fluctuations resembling Brownian motion. Heatmap of the true Brownian motion covariance, k(s,t) = min(s,t), over s and t from zero to one. Heatmap of the empirical covariance of Bayesian neural network samples with a Mercer prior, approximating the true Brownian motion covariance.
Bayesian neural networks with a Mercer prior can emulate Brownian motion sample paths. Figures 2 and 3, Alberts and Bilionis (2026).
03

Uncertainty quantification · Engineering applications

Working with experimental uncertainty.

Thermal protection materials

Laboratory measurements may cover only part of the temperature range experienced by a spacecraft’s insulation. I work on inferring thermal conductivity from temperature measurements using the heat equation and a probabilistic model of the unknown property.

This lets us examine how uncertainty grows beyond the measured regime and how different plausible conductivities affect thermal-protection predictions. The application also shows why the prior and the assumptions in the heat-transfer model matter.

Read the thermal-conductivity paper

Thermal conductivity versus temperature at 0.001 Torr. The inferred median, 95 percent credible interval, and posterior samples are compared with reference values. A dashed line separates the data and extrapolation ranges.
Conductivity inferred at 0.001 Torr. The blue band shows a 95% central credible interval; the dashed boundary separates the data range from extrapolation. Figure 2(b), Alberts, Thomas, Daryabeigi, and Bilionis (2026). View full-size figure.

Engine states and parameter calibration

To model intake manifold dynamics, I used IFT to reconstruct temperature and pressure while estimating physical parameters from noisy sensor data. Testing across engine cycles reveals where the model transfers well and where effects such as exhaust gas recirculation require a better physical description.

Intake manifold dynamics

Stochastic emissions

I have also contributed to modeling diesel particulate matter with a mean-reverting stochastic process. Engine variables determine its changing mean and volatility.

Particulate-matter modeling