Sauro Succi

Mihir Durve, Sibilla Orsini, Adriano Tiribocchi et al.

Tracking droplets in microfluidics is a challenging task. The difficulty arises in choosing a tool to analyze general microfluidic videos to infer physical quantities. The state-of-the-art object detector algorithm You Only Look Once (YOLO) and the object tracking algorithm Simple Online and Realtime Tracking with a Deep Association Metric (DeepSORT) are customizable for droplet identification and tracking. The customization includes training YOLO and DeepSORT networks to identify and track the objects of interest. We trained several YOLOv5 and YOLOv7 models and the DeepSORT network for droplet identification and tracking from microfluidic experimental videos. We compare the performance of the droplet tracking applications with YOLOv5 and YOLOv7 in terms of training time and time to analyze a given video across various hardware configurations. Despite the latest YOLOv7 being 10% faster, the real-time tracking is only achieved by lighter YOLO models on RTX 3070 Ti GPU machine due to additional significant droplet tracking costs arising from the DeepSORT algorithm. This work is a benchmark study for the YOLOv5 and YOLOv7 networks with DeepSORT in terms of the training time and inference time for a custom dataset of microfluidic droplets.

Mihir Durve, Adriano Tiribocchi, Fabio Bonaccorso et al.

Deep neural networks are rapidly emerging as data analysis tools, often outperforming the conventional techniques used in complex microfluidic systems. One fundamental analysis frequently desired in microfluidic experiments is counting and tracking the droplets. Specifically, droplet tracking in dense emulsions is challenging as droplets move in tightly packed configurations. Sometimes the individual droplets in these dense clusters are hard to resolve, even for a human observer. Here, two deep learning-based cutting-edge algorithms for object detection (YOLO) and object tracking (DeepSORT) are combined into a single image analysis tool, DropTrack, to track droplets in microfluidic experiments. DropTrack analyzes input videos, extracts droplets' trajectories, and infers other observables of interest, such as droplet numbers. Training an object detector network for droplet recognition with manually annotated images is a labor-intensive task and a persistent bottleneck. This work partly resolves this problem by training object detector networks (YOLOv5) with hybrid datasets containing real and synthetic images. We present an analysis of a double emulsion experiment as a case study to measure DropTrack's performance. For our test case, the YOLO networks trained with 60% synthetic images show similar performance in droplet counting as with the one trained using 100% real images, meanwhile saving the image annotation work by 60%. DropTrack's performance is measured in terms of mean average precision (mAP), mean square error in counting the droplets, and inference speed. The fastest configuration of DropTrack runs inference at about 30 frames per second, well within the standards for real-time image analysis.

Sauro Succi, Abhisek Ganguly, Santosh Ansumali

We inspect the analogy between machine-learning (ML) applications based on the transformer architecture without self-attention, {\it neural chains} hereafter, and discrete dynamical systems associated with discretised versions of neural integral and partial differential equations (NIE, PDE). A comparative analysis of the numerical solution of the (viscid and inviscid) Burgers and Eikonal equations via standard numerical discretization (also cast in terms of neural chains) and via PINN's learning is presented and commented on. It is found that standard numerical discretization and PINN learning provide two different paths to acquire essentially the same knowledge about the dynamics of the system. PINN learning proceeds through random matrices which bear no direct relation to the highly structured matrices associated with finite-difference (FD) procedures. Random matrices leading to acceptable solutions are far more numerous than the unique tridiagonal form in matrix space, which explains why the PINN search typically lands on the random ensemble. The price is a much larger number of parameters, causing lack of physical transparency (explainability) as well as large training costs with no counterpart in the FD procedure. However, our results refer to one-dimensional dynamic problems, hence they don't rule out the possibility that PINNs and ML in general, may offer better strategies for high-dimensional problems.

Sauro Succi

It is argued that the pursuit of an ever increasing number of weights in large-scale machine learning applications, besides being energetically unsustainable, is also conducive to manipulative strategies whereby Science is easily served as a strawman for economic and financial power. If machine learning is meant to serve science ahead of vested business interests, a paradigm shift is needed: from more weights and little insight to more insight and less weights.

Peter V. Coveney, Sauro Succi

We show that the scaling laws which determine the performance of large language models (LLMs) severely limit their ability to improve the uncertainty of their predictions. As a result, raising their reliability to meet the standards of scientific inquiry is intractable by any reasonable measure. We argue that the very mechanism which fuels much of the learning power of LLMs, namely the ability to generate non-Gaussian output distributions from Gaussian input ones, might well be at the roots of their propensity to produce error pileup, ensuing information catastrophes and degenerative AI behaviour. This tension between learning and accuracy is a likely candidate mechanism underlying the observed low values of the scaling components. It is substantially compounded by the deluge of spurious correlations pointed out by Calude and Longo which rapidly increase in any data set merely as a function of its size, regardless of its nature. The fact that a degenerative AI pathway is a very probable feature of the LLM landscape does not mean that it must inevitably arise in all future AI research. Its avoidance, which we also discuss in this paper, necessitates putting a much higher premium on insight and understanding of the structural characteristics of the problems being investigated.

Sauro Succi

We highlight a formal and substantial analogy between Machine Learning (ML) algorithms and discrete dynamical systems (DDS) in relaxation form. The analogy offers a transparent interpretation of the weights in terms of physical information-propagation processes and identifies the model function of the forward ML step with the local attractor of the corresponding discrete dynamics. Besides improving the explainability of current ML applications, this analogy may also facilitate the development of a new class ML algorithms with a reduced number of weights.

Jean-Michel Tucny, Mihir Durve, Sauro Succi

The rise of deep learning challenges the longstanding scientific ideal of insight - the human capacity to understand phenomena by uncovering underlying mechanisms. In many modern applications, accurate predictions no longer require interpretable models, prompting debate about whether explainability is a realistic or even meaningful goal. From our perspective in physics, we examine this tension through a concrete case study: a physics-informed neural network (PINN) trained on a rarefied gas dynamics problem governed by the Boltzmann equation. Despite the system's clear structure and well-understood governing laws, the trained network's weights resemble Gaussian-distributed random matrices, with no evident trace of the physical principles involved. This suggests that deep learning and traditional simulation may follow distinct cognitive paths to the same outcome - one grounded in mechanistic insight, the other in statistical interpolation. Our findings raise critical questions about the limits of explainable AI and whether interpretability can - or should-remain a universal standard in artificial reasoning.

Abhisek Ganguly, Alessandro Gabbana, Vybhav Rao et al.

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce corrections that impose constraints on the lower-order moments of the data distribution. This minimizes the discrepancy between the discrete and continuum representations of the data, in turn allowing to access more favorable energy landscapes, thus improving the accuracy of the interpolator. Our approach improves performance in both interpolation and regression tasks, even in high-dimensional spaces. Unlike traditional methods, it does not require empirical parameter tuning, making it particularly effective for handling noisy data. We also show that thanks to its local nature, the method offers computational and memory efficiency advantages over Radial Basis Function interpolators, especially for large datasets.

Abhisek Ganguly, Santosh Ansumali, Sauro Succi

Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression method with a single trainable parameter, to learn spatial derivatives with provable second-order accuracy in 1D. Two derivative-learning schemes are proposed: an explicit scheme based on the closed-form prediction expressions, and an implicit scheme that solves a perturbed linear system at the points of interest. The fully localized formulation enables efficient, noise-adaptive derivative estimation without requiring global system solving or heuristic smoothing. Both approaches exhibit quadratic convergence, matching second-order finite difference for clean data, along with a possible high-dimensional formulation. Preliminary results show that coupling KBR with conservative solvers enables stable shock capture in 1D hyperbolic PDEs, acting as a step towards solving PDEs on irregular point clouds in higher dimensions while preserving conservation laws.

Jean-Michel Tucny, Abhisek Ganguly, Santosh Ansumali et al.

It is shown that the weight matrices of transformer-based machine learning applications to the solution of two representative physical applications show a random-like character which bears no directly recognizable link to the physical and mathematical structure of the physical problem under study. This suggests that machine learning and the scientific method may represent two distinct and potentially complementary paths to knowledge, even though a strict notion of explainability in terms of direct correspondence between network parameters and physical structures may remain out of reach. It is also observed that drawing a parallel between transformer operation and (generalized) path-integration techniques may account for the random-like nature of the weights, but still does not resolve the tension with explainability. We conclude with some general comments on the hazards of gleaning knowledge without the benefit of Insight.

Paul Fischer, Sebastian Kaltenbach, Sergey Litvinov et al.

The Lattice Boltzmann method (LBM) offers a powerful and versatile approach to simulating diverse hydrodynamic phenomena, spanning microfluidics to aerodynamics. The vast range of spatiotemporal scales inherent in these systems currently renders full resolution impractical, necessitating the development of effective closure models for under-resolved simulations. Under-resolved LBMs are unstable, and while there is a number of important efforts to stabilize them, they often face limitations in generalizing across scales and physical systems. We present a novel, data-driven, multiagent reinforcement learning (MARL) approach that drastically improves stability and accuracy of coarse-grained LBM simulations. The proposed method uses a convolutional neural network to dynamically control the local relaxation parameter for the LB across the simulation grid. The LB-MARL framework is showcased in turbulent Kolmogorov flows. We find that the MARL closures stabilize the simulations and recover the energy spectra of significantly more expensive fully resolved simulations while maintaining computational efficiency. The learned closure model can be transferred to flow scenarios unseen during training and has improved robustness and spectral accuracy compared to traditional LBM models. We believe that MARL closures open new frontiers for efficient and accurate simulations of a multitude of complex problems not accessible to present-day LB methods alone.

Agastya P. Bhati, Shunzhou Wan, Dario Alfè et al.

The race to meet the challenges of the global pandemic has served as a reminder that the existing drug discovery process is expensive, inefficient and slow. There is a major bottleneck screening the vast number of potential small molecules to shortlist lead compounds for antiviral drug development. New opportunities to accelerate drug discovery lie at the interface between machine learning methods, in this case developed for linear accelerators, and physics-based methods. The two in silico methods, each have their own advantages and limitations which, interestingly, complement each other. Here, we present an innovative infrastructural development that combines both approaches to accelerate drug discovery. The scale of the potential resulting workflow is such that it is dependent on supercomputing to achieve extremely high throughput. We have demonstrated the viability of this workflow for the study of inhibitors for four COVID-19 target proteins and our ability to perform the required large-scale calculations to identify lead antiviral compounds through repurposing on a variety of supercomputers.