We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic interaction rules generate complex macroscopic behaviors. While our earlier work established a Gaussian process approach and convergence theory for single-species systems, and later extended to second-order models with alignment and energy-type interactions, the multi-species setting introduces new challenges: heterogeneous populations interact both within and across species, the number of unknown kernels grows, and asymmetric interactions such as predator-prey dynamics must be accommodated. We formulate the learning problem in a nonparametric Bayesian setting and establish rigorous statistical guarantees. Our analysis shows recoverability of the interaction kernels, provides quantitative error bounds, and proves statistical optimality of posterior estimators, thereby unifying and generalizing previous single-species theory. Numerical experiments confirm the theoretical predictions and demonstrate the effectiveness of the proposed approach, highlighting its advantages over existing kernel-based methods. This work contributes a complete statistical framework for data-driven inference of interaction laws in multi-species systems, advancing the broader multiscale modeling program of connecting microscopic particle dynamics with emergent macroscopic behavior.

Model-free diffusion planners have shown great promise for robot motion planning, but practical robotic systems often require combining them with model-based optimization modules to enforce constraints, such as safety. Naively integrating these modules presents compatibility challenges when diffusion's multi-modal outputs behave adversarially to optimization-based modules. To address this, we introduce Joint Model-based Model-free Diffusion (JM2D), a novel generative modeling framework. JM2D formulates module integration as a joint sampling problem to maximize compatibility via an interaction potential, without additional training. Using importance sampling, JM2D guides modules outputs based only on evaluations of the interaction potential, thus handling non-differentiable objectives commonly arising from non-convex optimization modules. We evaluate JM2D via application to aligning diffusion planners with safety modules on offline RL and robot manipulation. JM2D significantly improves task performance compared to conventional safety filters without sacrificing safety. Further, we show that conditional generation is a special case of JM2D and elucidate key design choices by comparing with SOTA gradient-based and projection-based diffusion planners. More details at: https://jm2d-corl25.github.io/.

The study presents a novel approach for quantifying cellular interactions in digital pathology using deep learning-based image cytometry. Traditional methods struggle with the diversity and heterogeneity of cells within tissues. To address this, we introduce the Spatial Interaction Potential (SIP) and the Co-Localization Index (CLI), leveraging deep learning classification probabilities. SIP assesses the potential for cell-to-cell interactions, similar to an electric field, while CLI incorporates distances between cells, accounting for dynamic cell movements. Our approach enhances traditional methods, providing a more sophisticated analysis of cellular interactions. We validate SIP and CLI through simulations and apply them to colorectal cancer specimens, demonstrating strong correlations with actual biological data. This innovative method offers significant improvements in understanding cellular interactions and has potential applications in various fields of digital pathology.

A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models.

This article focuses on Variational Inference (VI) for the Ising model in application to binary image denoising. As an example, consider a noisy gray scale image on the left and the denoised binary image on the right in the figure above. The Ising model is an example of a Markov Random Field (MRF) and it originated from statistical physics. The Ising model assumes that we have a grid of nodes, where each node can be in one of two states. In the case of binary images, you can think of each node as being a pixel with a black or white color.

Collaborative Innovation Center of Quantum Matter, Beijing, 100084, China (Dated: March 12, 2018) Motivated by the question that whether the empirical fitting of data by neural networks can yield the same structure of physical laws, we apply neural networks to a quantum mechanical two-body scattering problem with short-range potentials--a problem by itself plays an important role in many branches of physics. After training, the neural network can accurately predict s - wave scattering length, which governs the low-energy scattering physics. By visualizing the neural network, we show that it develops perturbation theory order by order when the potential depth increases, without solving the Schr odinger equation or obtaining the wavefunction explicitly. The result provides an important benchmark to the machine-assisted physics research or even automated machine learning physics laws. Human physicists have made great achievements in discovering laws of physics during the last several centuries.

School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China Recommender systems play an essential role in the modern business world. They recommend favorable items like books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their e fficiency without sacrificing accuracy. Exploiting the quantum to classical mapping inherent in the continuous-time quantum Monte Carlo methods, we construct a classical molecular gas model to reproduce the quantum distributions. We then utilize powerful molecular simulation techniques to propose e fficient quantum Monte Carlo updates. The recommender engine approach provides a general way to speed up the quantum impurity solvers. At the heart of every quantum Monte Carlo (QMC) method is a quantum to classical mapping.

A number of exact and approximate methods are available for inference calculations ingraphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables andpure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models.

A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wainwright et.

A number of exact and approximate methods are available for inference calculations in graphical models. Many recent approximate methods for graphs with cycles are based on tractable algorithms for tree structured graphs. Here we base the approximation on a different tractable model, planar graphs with binary variables and pure interaction potentials (no external field). The partition function for such models can be calculated exactly using an algorithm introduced by Fisher and Kasteleyn in the 1960s. We show how such tractable planar models can be used in a decomposition to derive upper bounds on the partition function of non-planar models. The resulting algorithm also allows for the estimation of marginals. We compare our planar decomposition to the tree decomposition method of Wainwright et.