pwc-archive/papers-with-abstracts huggingface dataset:
The two-clock problem in population dynamics
Authors: Kaan Öcal, Michael P. H. Stumpf
Date: 2025-04-29 00:00:00
Tasks: Epidemiology

Biological time can be measured in two ways: in generations and in physical time. When generation intervals differ between individuals, these two clocks diverge, which impedes our ability to relate mathematical models to real populations. In this paper we show that nevertheless, these disparate clocks become equivalent in the long run via a simple identity relating generational and physical time. This equivalence allows us to directly translate statements from mathematical models to the physical world and vice versa. As an application, we obtain a generalized Euler-Lotka equation linking the basic reproduction number $R_0$ to the growth rate, and derive several information-theoretic bounds on these quantities. We also show how the fitness of a lineage can be defined consistently in population models, with applications to microbial growth, epidemiology and population biology.
Continuous and discrete compartmental models for infectious disease
Authors: Gustavo A. Sousa, Diogo L. M. Souza, Enrique C. Gabrick, Patrício D. C. dos Reis, Lucas E. Bentivoglio, Antonio M. Batista, José D. Szezech Jr
Date: 2025-04-16 00:00:00
Tasks: Epidemiology

The study of infectious disease propagation is essential for understanding and controlling epidemics. One of the most useful tools for gaining insights into the spread of infectious diseases is mathematical modelling. In terms of mathematical epidemiology, the main models are based on compartments, such as SI, SIR, and SEIR. These models offer mathematical frameworks for representing the proliferation dynamics of various diseases, for instance flu and smallpox. In this work, we explore these models using two distinct mathematical approaches, Cellular Automata (CA) and ODEs. They are able to reproduce the spread dynamics of diseases with their own individuality. CA models incorporate the local interaction among individuals with discrete time and space, while ODEs provide a continuous and simplified view of a disease propagation in large and homogeneous populations. By comparing these two approaches, we find that the shape of the curves of all models is similar for both representations. Although, the growth rates differ between CA and ODE. One of our results is to show that the CA yields a power-law growth, while the ODE growth rate is well-represented by an exponential function. Furthermore, a substantial contribution of our work is using a hyperbolic tangent to fit the initial growth of infected individuals for all the considered models. Our results display a strong correlation between simulated data and adjusted function. We mainly address this successful result by the fact that the hyperbolic function captures both growing: the power-law (when considered the first terms of infinite sums) and combinations of exponential (when the hyperbolic function is written via exponential). Therefore, our work shows that when modelling a disease the choice of mathematical representation is crucial, in particular to model the onset of an epidemic.
Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework Without Data
Authors: Maximilian Stupp, P. S. Koutsourelakis
Date: 2025-04-29 00:00:00
Tasks: All

Coarse-grained (CG) models offer an effective route to reducing the complexity of molecular simulations, yet conventional approaches depend heavily on long all-atom molecular dynamics (MD) trajectories to adequately sample configurational space. This data-driven dependence limits their accuracy and generalizability, as unvisited configurations remain excluded from the resulting CG model. We introduce a data-free generative framework for coarse-graining that directly targets the all-atom Boltzmann distribution. Our model defines a structured latent space comprising slow collective variables, which are statistically associated with multimodal marginal densities capturing metastable states, and fast variables, which represent the remaining degrees of freedom with simple, unimodal conditional distributions. A potentially learnable, bijective map from the full latent space to the all-atom configuration space enables automatic and accurate reconstruction of molecular structures. The model is trained using an energy-based objective that minimizes the reverse Kullback-Leibler divergence, relying solely on the interatomic potential rather than sampled trajectories. A tempering scheme is used to stabilize training and promote exploration of diverse configurations. Once trained, the model can generate unbiased, one-shot equilibrium all-atom samples. We validate the method on two synthetic systems-a double-well potential and a Gaussian mixture-as well as on the benchmark alanine dipeptide. The model captures all relevant modes of the Boltzmann distribution, accurately reconstructs atomic configurations, and learns physically meaningful coarse-grained representations, all without any simulation data.
Enhanced Sampling, Public Dataset and Generative Model for Drug-Protein Dissociation Dynamics
Authors: Maodong Li, Jiying Zhang, Bin Feng, Wenqi Zeng, Dechin Chen, Zhijun Pan, Yu Li, Zijing Liu, Yi Isaac Yang
Date: 2025-04-25 00:00:00

Drug-protein binding and dissociation dynamics are fundamental to understanding molecular interactions in biological systems. While many tools for drug-protein interaction studies have emerged, especially artificial intelligence (AI)-based generative models, predictive tools on binding/dissociation kinetics and dynamics are still limited. We propose a novel research paradigm that combines molecular dynamics (MD) simulations, enhanced sampling, and AI generative models to address this issue. We propose an enhanced sampling strategy to efficiently implement the drug-protein dissociation process in MD simulations and estimate the free energy surface (FES). We constructed a program pipeline of MD simulations based on this sampling strategy, thus generating a dataset including 26,612 drug-protein dissociation trajectories containing about 13 million frames. We named this dissociation dynamics dataset DD-13M and used it to train a deep equivariant generative model UnbindingFlow, which can generate collision-free dissociation trajectories. The DD-13M database and UnbindingFlow model represent a significant advancement in computational structural biology, and we anticipate its broad applicability in machine learning studies of drug-protein interactions. Our ongoing efforts focus on expanding this methodology to encompass a broader spectrum of drug-protein complexes and exploring novel applications in pathway prediction.
Simulating biochemical reactions: The Linear Noise Approximation can capture non-linear dynamics
Authors: Frederick Truman-Williams, Giorgos Minas
Date: 2025-04-21 00:00:00
Tasks: Computational Efficiency, Epidemiology

There is a plethora of highly stochastic non-linear dynamical systems in fields such as molecular biology, chemistry, epidemiology, and ecology. Yet, none of the currently available stochastic models are both accurate and computationally efficient for long-term predictions of large systems. The Linear Noise Approximation (LNA) model for biochemical reaction networks is analytically tractable, which makes it computationally efficient for simulation, analysis, and inference. However, it is only accurate for linear systems and short-time transitions. Other methods can achieve greater accuracy across a wider range of systems, including non-linear ones, but lack analytical tractability. This paper seeks to challenge the prevailing view by demonstrating that the Linear Noise Approximation can indeed capture non-linear dynamics after certain modifications. We introduce a new framework that utilises centre manifold theory allowing us to identify simple interventions to the LNA that do not significantly compromise its computational efficiency. We develop specific algorithms for systems that exhibit oscillations or bi-stability and demonstrate their accuracy and computational efficiency across multiple examples.
High-performance training and inference for deep equivariant interatomic potentials
Authors: Chuin Wei Tan, Marc L. Descoteaux, Mit Kotak, Gabriel de Miranda Nascimento, Seán R. Kavanagh, Laura Zichi, Menghang Wang, Aadit Saluja, Yizhong R. Hu, Tess Smidt, Anders Johansson, William C. Witt, Boris Kozinsky, Albert Musaelian
Date: 2025-04-22 00:00:00
Tasks: Computational Efficiency

Machine learning interatomic potentials, particularly those based on deep equivariant neural networks, have demonstrated state-of-the-art accuracy and computational efficiency in atomistic modeling tasks like molecular dynamics and high-throughput screening. The size of datasets and demands of downstream workflows are growing rapidly, making robust and scalable software essential. This work presents a major overhaul of the NequIP framework focusing on multi-node parallelism, computational performance, and extensibility. The redesigned framework supports distributed training on large datasets and removes barriers preventing full utilization of the PyTorch 2.0 compiler at train time. We demonstrate this acceleration in a case study by training Allegro models on the SPICE 2 dataset of organic molecular systems. For inference, we introduce the first end-to-end infrastructure that uses the PyTorch Ahead-of-Time Inductor compiler for machine learning interatomic potentials. Additionally, we implement a custom kernel for the Allegro model's most expensive operation, the tensor product. Together, these advancements speed up molecular dynamics calculations on system sizes of practical relevance by up to a factor of 18.
Transferable Learning of Reaction Pathways from Geometric Priors
Authors: Juno Nam, Miguel Steiner, Max Misterka, Soojung Yang, Avni Singhal, Rafael Gómez-Bombarelli
Date: 2025-04-21 00:00:00

Identifying minimum-energy paths (MEPs) is crucial for understanding chemical reaction mechanisms but remains computationally demanding. We introduce MEPIN, a scalable machine-learning method for efficiently predicting MEPs from reactant and product configurations, without relying on transition-state geometries or pre-optimized reaction paths during training. The task is defined as predicting deviations from geometric interpolations along reaction coordinates. We address this task with a continuous reaction path model based on a symmetry-broken equivariant neural network that generates a flexible number of intermediate structures. The model is trained using an energy-based objective, with efficiency enhanced by incorporating geometric priors from geodesic interpolation as initial interpolations or pre-training objectives. Our approach generalizes across diverse chemical reactions and achieves accurate alignment with reference intrinsic reaction coordinates, as demonstrated on various small molecule reactions and [3+2] cycloadditions. Our method enables the exploration of large chemical reaction spaces with efficient, data-driven predictions of reaction pathways.
Aerodynamic and structural airfoil shape optimisation via Transfer Learning-enhanced Deep Reinforcement Learning
Authors: David Ramos, Lucas Lacasa, Eusebio Valero, Gonzalo Rubio
Date: 2025-05-05 00:00:00
Tasks: Computational Efficiency, Deep Reinforcement Learning, Transfer Learning

The main objective of this paper is to introduce a transfer learning-enhanced, multi-objective, deep reinforcement learning (DRL) methodology that is able to optimise the geometry of any airfoil based on concomitant aerodynamic and structural criteria. To showcase the method, we aim to maximise the lift-to-drag ratio $C_L/C_D$ while preserving the structural integrity of the airfoil -- as modelled by its maximum thickness -- and train the DRL agent using a list of different transfer learning (TL) strategies. The performance of the DRL agent is compared with Particle Swarm Optimisation (PSO), a traditional gradient-free optimisation method. Results indicate that DRL agents are able to perform multi-objective shape optimisation, that the DRL approach outperforms PSO in terms of computational efficiency and shape optimisation performance, and that the TL-enhanced DRL agent achieves performance comparable to the DRL one, while further saving substantial computational resources.
Geometry-Informed Neural Operator Transformer
Authors: Qibang Liu, Vincient Zhong, Hadi Meidani, Diab Abueidda, Seid Koric, Philippe Geubelle
Date: 2025-04-28 00:00:00
Tasks: Computational Efficiency, Decoder

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions for arbitrary geometries. GINOT encodes the surface points cloud of a geometry using a sampling and grouping mechanism combined with an attention mechanism, ensuring invariance to point order and padding while maintaining robustness to variations in point density. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its high accuracy and strong generalization capabilities for complex and arbitrary 2D and 3D geometries.
Quality-factor inspired deep neural network solver for solving inverse scattering problems
Authors: Yutong Du, Zicheng Liu, Miao Cao, Zupeng Liang, Yali Zong, Changyou Li
Date: 2025-04-29 00:00:00

Deep neural networks have been applied to address electromagnetic inverse scattering problems (ISPs) and shown superior imaging performances, which can be affected by the training dataset, the network architecture and the applied loss function. Here, the quality of data samples is cared and valued by the defined quality factor. Based on the quality factor, the composition of the training dataset is optimized. The network architecture is integrated with the residual connections and channel attention mechanism to improve feature extraction. A loss function that incorporates data-fitting error, physical-information constraints and the desired feature of the solution is designed and analyzed to suppress the background artifacts and improve the reconstruction accuracy. Various numerical analysis are performed to demonstrate the superiority of the proposed quality-factor inspired deep neural network (QuaDNN) solver and the imaging performance is finally verified by experimental imaging test.
Physics-guided and fabrication-aware inverse design of photonic devices using diffusion models
Authors: Dongjin Seo, Soobin Um, Sangbin Lee, Jong Chul Ye, Haejun Chung
Date: 2025-04-23 00:00:00
Tasks: Binarization, Denoising, global-optimization

Designing free-form photonic devices is fundamentally challenging due to the vast number of possible geometries and the complex requirements of fabrication constraints. Traditional inverse-design approaches--whether driven by human intuition, global optimization, or adjoint-based gradient methods--often involve intricate binarization and filtering steps, while recent deep learning strategies demand prohibitively large numbers of simulations (10^5 to 10^6). To overcome these limitations, we present AdjointDiffusion, a physics-guided framework that integrates adjoint sensitivity gradients into the sampling process of diffusion models. AdjointDiffusion begins by training a diffusion network on a synthetic, fabrication-aware dataset of binary masks. During inference, we compute the adjoint gradient of a candidate structure and inject this physics-based guidance at each denoising step, steering the generative process toward high figure-of-merit (FoM) solutions without additional post-processing. We demonstrate our method on two canonical photonic design problems--a bent waveguide and a CMOS image sensor color router--and show that our method consistently outperforms state-of-the-art nonlinear optimizers (such as MMA and SLSQP) in both efficiency and manufacturability, while using orders of magnitude fewer simulations (approximately 2 x 10^2) than pure deep learning approaches (approximately 10^5 to 10^6). By eliminating complex binarization schedules and minimizing simulation overhead, AdjointDiffusion offers a streamlined, simulation-efficient, and fabrication-aware pipeline for next-generation photonic device design. Our open-source implementation is available at https://github.com/dongjin-seo2020/AdjointDiffusion.
Least-Squares-Embedded Optimization for Accelerated Convergence of PINNs in Acoustic Wavefield Simulations
Authors: Mohammad Mahdi Abedi, David Pardo, Tariq Alkhalifah
Date: 2025-04-23 00:00:00

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from slow convergence and instability, particularly for high-frequency wavefields. For scattered acoustic wavefield simulation based on Helmholtz equation, we derive a hybrid optimization framework that accelerates training convergence by embedding a least-squares (LS) solver directly into the GD loss function. This formulation enables optimal updates for the linear output layer. Our method is applicable with or without perfectly matched layers (PML), and we provide practical tensor-based implementations for both scenarios. Numerical experiments on benchmark velocity models demonstrate that our approach achieves faster convergence, higher accuracy, and improved stability compared to conventional PINN training. In particular, our results show that the LS-enhanced method converges rapidly even in cases where standard GD-based training fails. The LS solver operates on a small normal matrix, ensuring minimal computational overhead and making the method scalable for large-scale wavefield simulations.
Low-dimensional representation of brain networks for seizure risk forecasting
Authors: Steven Rico-Aparicio, Martin Guillemaud, Alice Longhena, Vincent Navarro, Louis Cousyn, Mario Chavez
Date: 2025-05-01 00:00:00
Tasks: EEG, Robust classification

Identifying preictal states -- periods during which seizures are more likely to occur -- remains a central challenge in clinical computational neuroscience. In this study, we introduce a novel framework that embeds functional brain connectivity networks, derived from intracranial EEG (iEEG) recordings, into a low-dimensional Euclidean space. This compact representation captures essential topological features of brain dynamics and facilitates the detection of subtle connectivity changes preceding seizures. Using standard machine learning techniques, we define a dimensionless biomarker, $\mathcal{B}$, that discriminates between interictal (seizure-free) and preictal (within 24 hours of seizure) network states. Our method focuses on connectivity patterns among a subset of informative iEEG electrodes, enabling robust classification of brain states across time. We validate our approach using a leave-one-out cross-validation scheme and a pseudo-prospective forecasting strategy, assessing performance with metrics such as F1-score and balanced accuracy. Results show that low-dimensional Euclidean embeddings of iEEG connectivity yield interpretable and predictive markers of preictal activity, offering promising implications for real-time seizure forecasting and individualized therapeutic interventions.
Probability of collision in nonlinear dynamics by moment propagation
Authors: Théo Verhelst, Giacomo Acciarini, Dario Izzo, Francesco Biscani
Date: 2025-04-15 00:00:00
Tasks: Collision Avoidance

Estimating the probability of collision between spacecraft is crucial for risk management and collision-avoidance strategies. Current methods often rely on Gaussian assumptions and simplifications, which can be inaccurate in highly nonlinear scenarios. This paper presents a general and efficient approach for computing collision probabilities without relying on such assumptions. Using high-order multivariate Taylor polynomials, we propagate statistical moments of initial uncertainties to the point of closest approach between the spacecraft. To compute the probability of collision, we derive a semi-analytical expression for the probability density function (PDF) of the closest approach distance, inferred from the propagated moments using orthogonal polynomials. Tested on various short-term and long-term encounters in low-Earth orbit, our method accurately handles nonlinear dynamics, non-Gaussian uncertainties, and irregular distributions. This versatile framework advances space situational awareness by providing precise collision probability estimates in complex dynamical environments. Moreover, our methodology applies to any dynamical system with uncertainty in its initial state and is therefore not restricted to collision probability estimation.
Online learning to accelerate nonlinear PDE solvers: applied to multiphase porous media flow
Authors: Vinicius L S Silva, Pablo Salinas, Claire E Heaney, Matthew Jackson, Christopher C Pain
Date: 2025-04-25 00:00:00

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed method rely on four pillars: (i) dimensionless numbers as input parameters for the machine learning model, (ii) simplified numerical model (two-dimensional) for the offline training, (iii) dynamic control of a nonlinear solver tuning parameter (numerical relaxation), (iv) and online learning for real-time improvement of the machine learning model. This strategy decreases the number of nonlinear iterations by dynamically modifying a single global parameter, the relaxation factor, and by adaptively learning the attributes of each numerical model on-the-run. Furthermore, this work performs a sensitivity study in the dimensionless parameters (machine learning features), assess the efficacy of various machine learning models, demonstrate a decrease in nonlinear iterations using our method in more intricate, realistic three-dimensional models, and fully couple a machine learning model into an open-source multiphase flow simulator achieving up to 85\% reduction in computational time.
Online model learning with data-assimilated reservoir computers
Authors: Andrea Nóvoa, Luca Magri
Date: 2025-04-23 00:00:00
Tasks: Dimensionality Reduction, State Estimation, Time Series Forecasting

We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized autoregressive model to forecast reduced dynamics, here, a reservoir computer; (iii) online adaptation to update the reservoir computer (the model), here, ensemble sequential data assimilation.We demonstrate the framework on a wake past a cylinder governed by the Navier-Stokes equations, exploring the assimilation of full flow fields (projected onto POD modes) and sparse sensors. Three scenarios are examined: a na\"ive physical state estimation; a two-fold estimation of physical and reservoir states; and a three-fold estimation that also adjusts the model parameters. The two-fold strategy significantly improves ensemble convergence and reduces reconstruction error compared to the na\"ive approach. The three-fold approach enables robust online training of partially-trained reservoir computers, overcoming limitations of a priori training. By unifying data-driven reduced order modelling with Bayesian data assimilation, this work opens new opportunities for scalable online model learning for nonlinear time series forecasting.