RT @RMCrossley: My recent work (with co-authors @ruth_baker @PhilipMaini and Tommaso Lorenzi) studying the impact of volume-filling effects….

RT @SciKit_G: Our work using diffusive properties to characterise new liquid crystal phases in DNA is out in APL Materials now - it also in….

RT @M3sBiomath: Today was our Mini-Symposium regarding the combination of machine learning and mechanistic modeling organized with Andreas….

RT @yannik_schaelte: Very much enjoyed this 🌞summer school at @HCM_Bonn!.👩‍🏫Amazing lectures on stochastic models and inference; 👩‍🎓awesome….

A big thank you to @ruth_baker and @ProfMJSimpson for the great mentoring and collaboration :D.

By combining the data and PDE-FIND with Bayesian analysis, we open the door to inference in very large candidate to obtain a good model with rigorous uncertainty, while making computation feasible

Taken together, we find that by using PDE-FIND first to explore the space of models, we get a computational speed-up of about 40x compared to a naïve uniform prior, while the problem did not converge using Bayesian analysis without PDE-FIND!

Thankfully, this uncertainty is only present in some parameters, meaning we are confident in at least a part of the model! Hence, we can use Bayesian methods to explore which other bits of the model should be included, and which not.

Why do we get such a discrepancy? Noisy data makes it really hard for to identify different, but related models. The loss function that PDE-FIND optimizes (left) looks very different from a loss that compares models and data (right). (Red dots are estimated model parameters)

Using three test cases (unbiased motion, biased motion, and proliferation), we see that sometimes the algorithm will pick up a correct model, and sometimes it won’t!

If we could observe the PDE data, then we could derive the physical laws behind our random walk. But in real life, we only have our noisy measurements! What kind of predictions will we get?.

This image shows the observed density of agents moving according to a random walk model (left column), smoothed densities when we average over many data points (middle column) and a partial differential equation (PDE) that approximates the expected density at the same times

In this work, we use the popular PDE-FIND algorithm with noisy data that builds a “library” of possible terms in the model, and tries to learn the correct coefficients for each of these terms. For most problems, we want a simple model, so lots of these coefficients should be zero.

@ruth_baker @ProfMJSimpson Equation learning methods have been developed to learn a dynamical system that describes the evolution of some observed data. However, biological data is noisy and the predictions that result might be highly variable. 📈.

Very pleased to share my first paper "Bayesian uncertainty quantification for data-driven equation learning" with @ruth_baker and @ProfMJSimpson!. How do we combine noisy data with equation learning?A 🧵 (1/n).

RT @OxUniMaths: To thrive as a Graduate Student you need to learn how to pose questions. But you also need an environment that gives you th….

Happy Easter from our household @HertfordCollege 🥚🐰💐