arXiv subjects

Michael P. Brenner

Publications and source records attributed to Michael P. Brenner.

At least 19 recordsLinked to original sources

arXiv2026

Idea Search: Guiding Tree Search with Ideas to Explore Diverse Scientific Methods

Tree Search-based test-time scaling of LLMs is a powerful tool for automated scientific coding. However, pure Tree Search sometimes struggles with systematic exploration, becoming trapped in local optima, or unproductive loops, especially in the vast search space of scientific methods. To address this limitation, we propose Idea Search, a framework that systematically integrates a dynamic "Idea Bank" into Tree Search. Idea Search involves three steps: (1) decomposing existing methods into atomic ideas, (2) sampling from this bank of ideas to guide branches of code mutations, and (3) dynamically updating the bank with new ideas discovered through execution. On single-cell RNA-sequencing (scRNA-seq) batch integration, Idea Search reliably breaks the plateau of a strong pure Tree Search baseline, improving the mean score from 0.678 to 0.697 and reaching a best score of 0.728. We then characterize which design choices drive these gains: bank augmentation helps bandit sampling but not random sampling, "Exploratory" prompting that prioritizes new ideas surfaces the rare best-performing solutions, while increasing sampling-level exploration is counterproductive.

cs.LG↗

arXiv2026

Optimal feedback control under stepwise equilibration and partial observation

Many microscopic machines rely on noisy signals to direct nonequilibrium transformations and operate in a timescale-separated regime. We consider feedback protocols in which a system equilibrates between rapid, measurement-conditioned changes of its energy landscape. In this limit, the partially observable control problem reduces exactly to a finite-horizon Bellman recursion over Hamiltonian updates. For a harmonic trap translated to a prescribed target under noisy position measurements, we solve this recursion analytically. The optimal protocol balances its response to the estimated fluctuation against progress toward the target, exploiting information early while enforcing the endpoint near the deadline. The minimum work decomposes into a positive thermodynamic-length transport cost and a negative information-enabled extraction term set by the fraction of equilibrium fluctuations resolved by the measurement. When a fixed intervention cost exceeds the asymptotic extraction per cycle, it selects a finite optimal number of cycles. We show that, in this translated harmonic case, the minimum thermodynamic cost of creating and resetting the measurement record always exceeds this threshold, making the optimal cycle count finite and the net work non-negative for any measurement channel.

cond-mat.stat-mech↗

arXiv2026

Probabilistic Seasonal Streamflow Forecasting Across California's Sierra Nevada Watersheds with Agentic AI

Accurate seasonal runoff forecasts are critical for managing California's reservoirs and water supply for millions of its residents. Winter snow accumulation provides a strong source of predictability of snowmelt-based runoff in the spring and summer months, but progressive hydroclimatic changes in the Sierra Nevada are altering its timing and volume. These changes reduce the skill of statistical forecasts trained on historical data, highlighting the need for improved forecasting systems that can capture the changing dynamics of snowmelt. Here we demonstrate that a collaborative workflow between an agentic AI assistant and an automated code-mutation system, both powered by large language models, can accelerate the development of competitive seasonal runoff forecasting systems. In our framework, the AI agent discovers relevant datasets, synthesizes domain knowledge from prior forecasting competitions and the scientific literature, and explores the space of model architectures, while the code-mutation system refines each of the solutions explored by the agent through Monte Carlo Tree Search over the code space. The resulting system forecasts monthly Full Natural Flow (FNF) at 1- to 6-month lead times across 23 Sierra Nevada watersheds using an adaptive ensemble of three XGBoost quantile regression sub-models with physics-informed feature engineering. Evaluated against California's operational Bulletin 120 forecasts over 2021-2025, the agent-evolved model achieves superior skill for early-season cumulative April-July runoff predictions, reducing watershed-averaged quantile forecast error by up to 29%, and offering a new paradigm for AI-driven scientific model development in the geosciences.

physics.ao-ph↗

arXiv2026

Optimized Three-Dimensional Photovoltaic Structures with LLM guided Tree Search

We present a case study for how AI coding systems can be used to generate novel scientific hypotheses. We combine a generic coding agent (Google's AntiGravity) with an LLM-driven tree search algorithm (Empirical Research Assistance / ERA) to autonomously generate high-efficiency three-dimensional photovoltaic (3DPV) structures that overcome losses limiting flat solar panels at mid-latitudes. These structures operate by presenting favorable angles to the sun throughout the day, and for illustrative purposes we focus on optimizing performance for a single solar day. Our workflow begins by using AntiGravity to reproduce calculations \cite{bernardi2012solar} showing that 3DPV can have energy densities much higher than stationary flat PV panels. We use these initial designs as the starting point for large scale tree search, where we seek improved solutions and score them for their diurnal yield. The initial tree search leads to nominally more efficient solutions, yet they are caused by algorithmic reward hacking, arising from non-physical design features such as structurally levitating disconnected tiers and exploitations of the discretizations in the optics solver. To counteract this, we develop a workflow where the coding agent iteratively patches the physics engine with constraints to eliminate reward hacking. With reward-hacking eliminated, ERA discovers a series of designs with various constraints and improved performance, including optimal designs with different fixed collector areas, optimizing zenith tracking and avoiding self shadowing. Combining coding agents with tree search (ERA) provides a powerful platform for scientific discovery, for problems whose solutions can be empirically evaluated with a score function.

cs.CL↗

arXiv2026

Prospective multi-pathogen disease forecasting using autonomous LLM-guided tree search

Probabilistic forecasting of infectious diseases is crucial for public health but relies on labor-intensive manual model curation by expert modeling teams. This bespoke development bottlenecks scalability to granular geographic resolutions or emerging pathogens. Here, we present an autonomous system using Large Language Model (LLM)-guided tree search to iteratively generate, evaluate, and optimize executable forecasting software. In a fully prospective, real-time evaluation during the 2025-2026 US respiratory season, the system autonomously discovered methodologically diverse models for influenza, COVID-19, and respiratory syncytial virus (RSV). Aggregating these machine-generated models yielded an ensemble that consistently matched or outperformed the gold-standard, human-curated Centers for Disease Control and Prevention (CDC) hub ensembles out-of-sample. The system successfully navigated data-scarce "cold start" scenarios for RSV. Moreover, controlled retrospective ablations revealed that optimizing log-scale distance metrics prevents reward hacking, while an automated judge-in-the-loop ensures structural fidelity to complex scientific theories. By autonomously translating epidemiological theory into accurate, transparent code, this framework overcomes the modeling labor bottleneck, enabling rapid deployment of expert-level disease forecasting at unprecedented scales.

cs.AI↗

arXiv2026

Solving an Open Problem in Theoretical Physics using AI-Assisted Discovery

This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language model with a systematic Tree Search (TS) framework and automated numerical feedback, that successfully derived novel, exact analytical solutions for the power spectrum of gravitational radiation emitted by cosmic strings. Specifically, the agent evaluated the core integral $I(N,\alpha)$ for arbitrary loop geometries, directly improving upon recent AI-assisted attempts \cite{BCE+25} that only yielded partial asymptotic solutions. To substantiate our methodological claims regarding AI-accelerated discovery and to ensure transparency, we detail system prompts, search constraints, and intermittent feedback loops that guided the model. The agent identified a suite of 6 different analytical methods, the most elegant of which expands the kernel in Gegenbauer polynomials $C_l^{(3/2)}$ to naturally absorb the integrand's singularities. The methods lead to an asymptotic result for $I(N,\alpha)$ at large $N$ that both agrees with numerical results and also connects to the continuous Feynman parameterization of Quantum Field Theory. We detail both the algorithmic methodology that enabled this discovery and the resulting mathematical derivations.

cs.AI↗

arXiv2026

Accelerating Scientific Research with Gemini: Case Studies and Common Techniques

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

cs.CL↗

arXiv2026

Gradient-based optimization of exact stochastic kinetic models

Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require optimizing over trajectories generated by the Stochastic Simulation Algorithm, but the discrete reaction events involved are inherently non-differentiable. We present an approach based on straight-through Gumbel-Softmax estimation that maintains exact stochastic simulations in the forward pass while approximating gradients through a continuous relaxation applied only in the backward pass. We demonstrate robust performance on parameter inference in stochastic gene expression, first recovering kinetic rates of telegraph promoter models from both moment statistics and full steady-state distributions across diverse and challenging synthetic parameter regimes, then inferring the kinetic parameters of a four-state promoter model from experimental single-molecule RNA timecourse measurements. We further apply the method to inverse design in stochastic thermodynamics, optimizing non-equilibrium currents in an interacting particle system under kinetic resource constraints and recovering known analytical bounds. The ability to efficiently differentiate through exact stochastic simulations provides a foundation for systematic scalable inference and rational design across the many domains governed by continuous-time Markov dynamics.

physics.comp-ph↗

arXiv2025

Iterative improvement of free energy landscape reconstructions with optimal protocols derived from differentiable simulations

Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing, non-equilibrium driving protocols for estimating these landscapes require a priori knowledge of the landscape. Here, we present an alternative: an iterative algorithm for optimizing full free energy landscape reconstructions which can be used alongside experiments on unknown landscapes. Our approach (i) takes experimental or simulated trajectory data; (ii) reconstructs an `approximate' energy landscape; (iii) derives optimal control protocols from low-dimensional differentiable Brownian dynamics simulations on the candidate landscape using automatic differentiation; (iv) re-runs the experiment or simulation using the updated protocol; and (v) iterates until convergence. Using this approach, we recover known benchmarks from the literature and probe far-from-equilibrium regimes for symmetric, asymmetric, and triple-well energy landscapes under both 1- and 2-dimensional control. Our control protocols -- derived with no a priori knowledge of the energy landscape -- yield substantially reduced variance and bias in free energy landscape reconstructions compared to naive linear protocols.

physics.bio-ph↗

arXiv2025

Generalizing PDE Emulation with Equation-Aware Neural Operators

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for equation-aware emulation that generalizes to unseen PDEs, conditioning a neural model on a vector encoding representing the terms in a PDE and their coefficients. We present a baseline of four distinct modeling technqiues, trained on a family of 1D PDEs from the APEBench suite. Our approach achieves strong performance on parameter sets held out from the training distribution, with strong stability for rollout beyond the training window, and generalization to an entirely unseen PDE. This work was developed as part of a broader effort exploring AI systems that automate the creation of expert-level empirical software for scorable scientific tasks. The data and codebase are available at https://github.com/google-research/generalized-pde-emulator.

cs.LG↗

arXiv2025

Expert Evaluation of LLM World Models: A High-$T_c$ Superconductivity Case Study

Large Language Models (LLMs) show great promise as a powerful tool for scientific literature exploration. However, their effectiveness in providing scientifically accurate and comprehensive answers to complex questions within specialized domains remains an active area of research. Using the field of high-temperature cuprates as an exemplar, we evaluate the ability of LLM systems to understand the literature at the level of an expert. We construct an expert-curated database of 1,726 scientific papers that covers the history of the field, and a set of 67 expert-formulated questions that probe deep understanding of the literature. We then evaluate six different LLM-based systems for answering these questions, including both commercially available closed models and a custom retrieval-augmented generation (RAG) system capable of retrieving images alongside text. Experts then evaluate the answers of these systems against a rubric that assesses balanced perspectives, factual comprehensiveness, succinctness, and evidentiary support. Among the six systems two using RAG on curated literature outperformed existing closed models across key metrics, particularly in providing comprehensive and well-supported answers. We discuss promising aspects of LLM performances as well as critical short-comings of all the models. The set of expert-formulated questions and the rubric will be valuable for assessing expert level performance of LLM based reasoning systems.

cond-mat.supr-con↗

arXiv2025

Meshless solutions of PDE inverse problems on irregular geometries

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true domain. We find the coefficients of the basis expansion by solving an optimization problem whereby both the equations, the boundary conditions and any optimization targets are enforced by a loss function, building on a key idea from Physics-Informed Neural Networks (PINNs). Since the representation of the function natively has exponential convergence, so does the solution of the optimization problem, as long as it can be solved efficiently. We find empirically that the optimization protocols developed for machine learning find solutions with exponential convergence on a wide range of equations. The method naturally allows for the incorporation of data assimilation by including additional terms in the loss function, and for the efficient solution of optimization problems over the PDE solutions.

math.NA↗

arXiv2025

Learning constitutive models and rheology from partial flow measurements

Constitutive laws relate fluid stress to deformation and underpin predictions of non-Newtonian behavior in industrial and biological fluids. Standard characterization relies on measurements in idealized flows that often miss physics relevant to complex geometries. Existing data-driven methods overfit sparse data, lack geometry portability, or presuppose constitutive forms. To unify measurement and constitutive discovery, we developed an end-to-end framework that leverages automatic differentiation through a full physics simulation. By embedding a frame-invariant tensor basis neural network (TBNN) within a differentiable non-Newtonian solver, we learn constitutive laws from any flow observable without presupposing a specific model, spanning generalized Newtonian, viscoelastic, and yield-stress behavior. Unlike coordinate-dependent methods, learning local material response enables accurate flow predictions in unseen geometries and conditions without retraining. We then distill the TBNN closure into symbolic form via automated model selection using the Bayesian Information Criterion, extracting interpretable physical parameters. This work establishes a foundation for comprehensive characterization of complex fluids directly within their operating environment ("digital rheometry") with broad applicability to constitutive discovery across engineering and the physical sciences.

physics.flu-dyn↗

arXiv2025

General Purpose Inverse Design of Heterogeneous Finite-Sized Assemblies

Designing heterogeneous, self-assembling systems is a central challenge in soft matter and biology. We present a framework that uses gradient-based optimization to invert an analytical yield calculation, tuning systems toward target equilibrium yields. We design systems ranging from simple dimers to temperature-controlled shells to polymerizing systems, achieving precise control of self- and non-self-limiting assemblies. By operating directly on closed-form calculations, our framework bypasses trajectory-based instabilities and enables efficient optimization in otherwise challenging regimes.

cond-mat.soft↗

arXiv2025

CMT-Benchmark: A Benchmark for Condensed Matter Theory Built by Expert Researchers

Large language models (LLMs) have shown remarkable progress in coding and math problem-solving, but evaluation on advanced research-level problems in hard sciences remains scarce. To fill this gap, we present CMT-Benchmark, a dataset of 50 problems covering condensed matter theory (CMT) at the level of an expert researcher. Topics span analytical and computational approaches in quantum many-body, and classical statistical mechanics. The dataset was designed and verified by a panel of expert researchers from around the world. We built the dataset through a collaborative environment that challenges the panel to write and refine problems they would want a research assistant to solve, including Hartree-Fock, exact diagonalization, quantum/variational Monte Carlo, density matrix renormalization group (DMRG), quantum/classical statistical mechanics, and model building. We evaluate LLMs by programmatically checking solutions against expert-supplied ground truth. We developed machine-grading, including symbolic handling of non-commuting operators via normal ordering. They generalize across tasks too. Our evaluations show that frontier models struggle with all of the problems in the dataset, highlighting a gap in the physical reasoning skills of current LLMs. Notably, experts identified strategies for creating increasingly difficult problems by interacting with the LLMs and exploiting common failure modes. The best model, GPT5, solves 30\% of the problems; average across 17 models (GPT, Gemini, Claude, DeepSeek, Llama) is 11.4\pm2.1\%. Moreover, 18 problems are solved by none of the 17 models, and 26 by at most one. These unsolved problems span Quantum Monte Carlo, Variational Monte Carlo, and DMRG. Answers sometimes violate fundamental symmetries or have unphysical scaling dimensions. We believe this benchmark will guide development toward capable AI research assistants and tutors.

cs.LG↗

arXiv2025

Fundamental Scaling Constraints for Equilibrium Molecular Computing

Molecular computing promises massive parallelization to explore solution spaces, but so far practical implementations remain limited due to off-target binding and exponential proliferation of competing structures. Here, we investigate the theoretical limits of equilibrium self-assembly systems for solving computing problems, focusing on the directed Hamiltonian Path Problem (HPP) as a benchmark for NP-complete problems. The HPP is encoded via particles with directional lock-key patches, where self-assembled chains form candidate solution paths. We determine constraints on the required energy gap between on-target and off-target binding for the HPP to be encoded and solved. We simultaneously examine whether components with the required energy gap can be designed. Combining these results yields a phase diagram identifying regions where HPP instances are both encodable and solvable. These results establish fundamental upper bounds on equilibrium molecular computation and highlight the necessity of non-equilibrium approaches for scalable molecular computing architectures.

cond-mat.soft↗

arXiv2025

EEFSUVA: A New Mathematical Olympiad Benchmark

Recent breakthroughs have spurred claims that large language models (LLMs) match gold medal Olympiad to graduate level proficiency on mathematics benchmarks. In this work, we examine these claims in detail and assess the extent to which current benchmarks capture genuine LLM mathematical reasoning. The composition of these benchmarks, primarily drawing from the International Mathematics Olympiad (IMO) and related competitions, may overstate models reasoning ability due to potential data contamination and a narrow focus on familiar problem types. To enable a more holistic assessment of mathematical understanding, we introduce EEFSUVA, a novel benchmark curated from under circulated regional and national Olympiads of Eastern Europe and the countries from the former Soviet Union. These contests feature problems of comparable difficulty to the IMO and are renowned for demanding nonstandard problem-solving techniques, yet their problems are far less prevalent in online corpora. Preliminary results suggest that even state-of-the-art LLMs exhibit a notable performance decline on EEFSUVA relative to other Olympiad-style benchmarks. These findings also suggest the potential importance of broader evaluation datasets for a fuller assessment of mathematical reasoning and for guiding future model development.

cs.CL↗

arXiv2025

Combinatorial decision-making driven by multicomponent surface condensates

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules self-organize by phase transitions into coexisting spatial compartments called condensates, often on cellular surfaces such as chromatin and membranes. In this paper, we demonstrate that multicomponent fluids can be designed to recruit distinct condensates to surfaces with differing compositions, performing a form of surface classification by condensation. We draw an analogy to multidimensional classification in machine learning and explore how hidden species, analogous to hidden nodes, expand the expressivity and capacity of these interacting ensembles to facilitate complex decision boundaries. By simply changing levels of individual species, we find that the same molecular repertoire can be reprogrammed to solve new tasks. Together, our findings suggest that the physical processes underlying biomolecular condensates can encode and drive adaptive information processing beyond compartmentalization.

physics.bio-ph↗