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📰 "Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis"
arxiv.org/abs/2505.11491 #Physics.Comp-Ph #Dynamics #Matrix #Cs.Lg

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arXiv.orgPotential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysisThis study critically examines the performance of physics-informed machine learning (PIML) approaches for traffic flow modeling, defining the failure of a PIML model as the scenario where it underperforms both its purely data-driven and purely physics-based counterparts. We analyze the loss landscape by perturbing trained models along the principal eigenvectors of the Hessian matrix and evaluating corresponding loss values. Our results suggest that physics residuals in PIML do not inherently hinder optimization, contrary to a commonly assumed failure cause. Instead, successful parameter updates require both ML and physics gradients to form acute angles with the quasi-true gradient and lie within a conical region. Given inaccuracies in both the physics models and the training data, satisfying this condition is often difficult. Experiments reveal that physical residuals can degrade the performance of LWR- and ARZ-based PIML models, especially under highly physics-driven settings. Moreover, sparse sampling and the use of temporally averaged traffic data can produce misleadingly small physics residuals that fail to capture actual physical dynamics, contributing to model failure. We also identify the Courant-Friedrichs-Lewy (CFL) condition as a key indicator of dataset suitability for PIML, where successful applications consistently adhere to this criterion. Lastly, we observe that higher-order models like ARZ tend to have larger error lower bounds than lower-order models like LWR, which is consistent with the experimental findings of existing studies.

📰 "Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schr\"odinger Bridge"
arxiv.org/abs/2505.11197 #Dynamics #Q-Bio.Qm #Math.Oc #Cs.Lg #Cell

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arXiv.orgModeling Cell Dynamics and Interactions with Unbalanced Mean Field Schrödinger BridgeModeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schrödinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schrödinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy.

Today I have been learning the basics of λ-calculus

α- equivalence

β- reduction

... all necessary basics before I can get the cool stuff about using type checkers to prove maths (I think).

learning the basics of λ-calculus

book says the term λx. (x x) has 4 sub terms :

λx. (xx)
(xx)
left x in (x x)
right x in (x x)

BUT not the x in λx

why is this?

is it because the y in λy (something) is only pointing out which variable in (something) is the "abstract" variable, or the one that takes on values to whatever (something) is applied to?

in which case why is λx. (x x) different to (xx) ?

I'm on the last chapter of the University of Finland's Haskell mooc course.

Of all the languages I've tried over 30+ years

* #haskell pushed me to think in terms of higher-order functions - and also to value the importance of types

* #prolog was the first to make think declaratively and to solve problems by riding on its internal (search) mechanism

* #6502 on the BBC micro gave me empathy for what's happening "on metal"

* #lean opened my eyes to the power of #cs theory to check maths