Search NASA⌕ Search

SEARCH · Search NASA

Results for “Trainability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2024

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗
DOE OSTI2025

Dendritic Computing with Multigate Ferroelectric Field-Effect Transistors

Although inspired by neuronal systems in the brain, artificial neural networks generally employ point-neurons, which offer computational complexity far less than that of their biological counterparts. Neurons have dendritic arbors that connect to different sets of synapses and offer local nonlinear accumulation – playing a pivotal role in processing and learning. Inspired by this, we propose a novel neuron design based on a multigate ferroelectric field-effect transistor that mimics dendrites. It leverages ferroelectric nonlinearity for local computations within dendritic branches while utilizing the transistor action to generate the neuronal output. The branched architecture enables smaller crossbar arrays in hardware integration, improving efficiency. Using an experimentally calibrated device-circuit-algorithm cosimulation framework, we demonstrate that networks incorporating our dendritic neurons achieve superior performance compared to much larger networks without dendrites (∼ 17× fewer trainable weight parameters). These findings suggest that dendritic hardware can significantly improve computational efficiency and learning capacity of neuromorphic systems optimized for edge applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit’s generators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Operating advanced scientific instruments with AI agents that learn on the job

Advanced scientific user facilities, such as next generation X-ray light sources and self-driving laboratories, are revolutionizing scientific discovery by automating routine tasks and enabling rapid experimentation and characterizations. However, these facilities must continuously evolve to support new experimental workflows, adapt to diverse user projects, and meet growing demands for more intricate instruments and experiments. This continuous development introduces significant operational complexity, necessitating a focus on usability, reproducibility, and intuitive human-instrument interaction. In this work, we explore the integration of agentic AI, powered by Large Language Models (LLMs), as a transformative tool to achieve this goal. We present our approach to developing a human-in-the-loop pipeline for operating advanced instruments including an X-ray nanoprobe beamline and an autonomous robotic station dedicated to the design and characterization of materials. Specifically, we evaluate the potential of various LLMs as trainable scientific assistants for orchestrating complex, multi-task workflows, which also include multimodal data, optimizing their performance through optional human input and iterative learning. We demonstrate the ability of AI agents to bridge the gap between advanced automation and user-friendly operation, paving the way for more adaptable and intelligent scientific facilities.

Large Language Models↗
DOE OSTI2024

Quantum subspace expansion in the presence of hardware noise

Finding ground state energies on current quantum processing units (QPUs) using algorithms such as the variational quantum eigensolver (VQE) continues to pose challenges. Hardware noise severely affects both the expressivity and trainability of parameterized quantum circuits, limiting them to shallow depths in practice. Here, we demonstrate that both issues can be addressed by synergistically integrating VQE with a quantum subspace expansion, allowing for an optimal balance between quantum and classical computing capabilities and costs. We perform a systematic benchmark analysis of the iterative quantum-assisted eigensolver in the presence of hardware noise. We determine ground state energies of 1D and 2D mixed-field Ising spin models on noisy simulators and the IBM QPUs ibmq_quito (5 qubits) and ibmq_guadalupe (16 qubits). To maximize accuracy, we propose a suitable criterion to select the subspace basis vectors according to the trace of the noisy overlap matrix. Finally, we show how to systematically approach the exact solution by performing controlled quantum error mitigation based on probabilistic error reduction on the noisy backend fake_guadalupe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Pre-training Vision Models for the Classification of Alerts from Wide-field Time-domain Surveys

Modern wide-field time-domain surveys facilitate the study of transient, variable and moving phenomena by conducting image differencing and relaying alerts to their communities. Machine learning tools have been used on data from these surveys and their precursors for more than a decade, and convolutional neural networks (CNNs), which make predictions directly from input images, saw particularly broad adoption through the 2010s. Since then, continually rapid advances in computer vision have transformed the standard practices around using such models. It is now commonplace to use standardized architectures pre-trained on large corpora of everyday images (e.g., ImageNet). In contrast, time-domain astronomy studies still typically design custom CNN architectures and train them from scratch. Here, we explore the effects of adopting various pre-training regimens and standardized model architectures on the performance of alert classification. We find that the resulting models match or outperform a custom, specialized CNN like what is typically used for filtering alerts. Moreover, our results show that pre-training on galaxy images from Galaxy Zoo tends to yield better performance than pre-training on ImageNet or training from scratch. We observe that the design of standardized architectures are much better optimized than the custom CNN baseline, requiring significantly less time and memory for inference despite having more trainable parameters. On the eve of the Legacy Survey of Space and Time and other image-differencing surveys, these findings advocate for a paradigm shift in the creation of vision models for alerts, demonstrating that greater performance and efficiency, in time and in data, can be achieved by adopting the latest practices from the computer vision field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Space-Charge-Limited van der Waals Spin Transistor

Integrating semiconducting and magnetic materials could combine transistorlike operation with nonvolatility and enable architectures such as logic in memory. Here, in this work, we employ correlated electrical transport and scanning nitrogen-vacancy center magnetic imaging to elucidate a spin transistor concept that amalgamates vertical and lateral hopping transport inside a 2D antiferromagnetic semiconductor, mechanistically distinct from vertical tunneling devices. Our device, based on a monolayer-bilayer junction in CrSBr, displays giant, gate-tunable magnetoresistance driven by the dual action of electrostatic doping on space-charge-limited lateral conduction and interlayer exchange coupling. Moreover, we visualize a field-trainable, layer-sharing effect that selects between coherent or domain-wall reversal at the spin-flip transition, enabling multilevel, memristive conductance states. Our layer-dependent space charge mechanism for convergent electrical and magnetic control opens opportunities to address limitations in contemporary computing.

2-dimensional systems↗
DOE OSTI2025

A Two-Stage Quantum Reinforcement Learning Method for Multi-Objective Transmission Switching

Multi-objective transmission switching (MO-TS) problems involve the strategic reconfiguration of network topology to simultaneously optimize multiple objectives. As the system scale increases, finding feasible solutions becomes increasingly challenging due to the problem's nonlinearity and high computational complexity. To address these challenges, this paper proposes a two-stage quantum reinforcement learning method that leverages potential quantum advantages for MO-TS. In the first stage, candidate switching lines are identified using a graph-theoretical approach to reduce the problem's dimensionality. The second stage introduces a quantum-classical reinforcement learning framework, where a learnable measurement-based CNN-ResVQC architecture is developed to effectively reduce the input dimension for quantum processing, mitigate vanishing gradients, and enhance trainability while improving the quantum circuit's flexibility in modeling complex decision policies for MO-TS. Numerical studies on IEEE 14-bus, 57-bus, and 118-bus systems demonstrate that the proposed algorithm achieves superior training stability and faster convergence with approximately 1% of the network parameters required by classical algorithms, highlighting its effectiveness, efficiency, and scalability. Furthermore, the practicality is validated through its stable convergence under three common quantum noise channels.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

ATTNChecker: Highly-Optimized Fault Tolerant Attention for Large Language Model Training

Large Language Models (LLMs) have demonstrated remarkable performance in various natural language processing tasks. However, the training of these models is computationally intensive and susceptible to faults, particularly in the attention mechanism, which is a critical component of transformer-based LLMs. In this paper, we investigate the impact of faults on LLM training, focusing on INF, NaN, and near-INF values in the computation results with systematic fault injection experiments. We observe the propagation patterns of these errors, which can trigger non-trainable states in the model and disrupt training, forcing the procedure to load from checkpoints. To mitigate the impact of these faults, we propose ATTNChecker, the first Algorithm-Based Fault Tolerance (ABFT) technique tailored for the attention mechanism in LLMs. ATTNChecker is designed based on fault propagation patterns of LLM and incorporates performance optimization to adapt to both system reliability and model vulnerability while providing lightweight protection for fast LLM training. Evaluations on four LLMs show that ATTNChecker on average incurs on average 7% overhead on training while detecting and correcting all extreme errors. Compared with the state-of-the-art checkpoint/restore approach, ATTNChecker reduces recovery overhead by up to 49×.

Liang, Yuhang [University of Alabama - Birmingham]↗
DOE OSTI2025

CAFE AU LAIT: Compute-Aware Federated Augmented Low-Rank AI Training

Federated finetuning is crucial for unlocking the knowledge embedded in pretrained Large Language Models (LLMs) when data are geographically distributed across clients. Unlike finetuning with data from a single institution, federated finetuning allows collaboration across multiple institutions, enabling the utilization of diverse and decentralized datasets while preserving data privacy. Given the high computing costs of LLM training and the emphasis on energy efficiency in Federated Learning (FL), Low-Rank Adaptation (LoRA) has emerged as a widely adopted algorithm due to its significantly reduced number of trainable parameters. However, this assumes that all data silos have the necessary computing resources to compute local updates of LLMs. Nevertheless, in practice, the computing resources across clients are highly heterogeneous: while some may have access to hundreds of GPUs, others might have limited or no GPU access. Recently, federated finetuning using synthetic data has been proposed, allowing clients to participate in a collaborative training run without training LLMs locally. However, our experimental results reveal a performance gap between models trained using synthetic data and those trained using local updates. Motivated by the observed heterogeneity in computing resources and the performance gap, we propose a novel two-stage algorithm that leverages the storage and computing capabilities of a strong server. In the first stage, under the coordination of the strong server, clients with limited computing resources collaborate to generate synthetic data, which is transferred to and stored on the strong server. In the second stage, the strong server uses this synthetic data on behalf of the resource-constrained clients to perform federated LoRA finetuning alongside clients with sufficient computing resources. This approach ensures that all clients can participate in the finetuning process. Experimental results demonstrate that incorporating local updates from even a small fraction of clients improves performance compared to using synthetic data for all clients. Furthermore, we incorporate the Gaussian mechanism in both stages to guarantee client-level differential privacy.

Wang, Jiayi [ORNL]↗
DOE OSTI2025

Intercomparison of Deep Learning Model Architectures for Atmospheric River Prediction

With a rapid surge in the application of machine learning (ML) for a diverse range of tasks in climate science, the present study addresses a challenge for climate scientists when selecting the optimal ML or deep learning (DL) architecture for a given application. In particular, a DL intercomparison study was performed with a focus on forecasting the position of atmospheric rivers (ARs) on short-range time scales (up to 5-day lead times). AR predictions from multiple DL architectures, including various types of convolutional autoencoders and a vision transformer (ViT), were compared against ECMWF ERA5 reanalysis and hindcasts from a global climate model. DL models with similar trainable parameters were trained on ERA5 reanalysis data and AR positions derived from a thresholding algorithm to ensure a fair comparison among the DL models. Each model’s performance and accuracy in forecasting AR location and key input fields within a 5-day window were assessed using metrics of root-mean-square error, anomaly correlation, and mean intersection over union. The ViT architecture outperformed other autoencoder models in most of the metrics. Incorporating additional meteorological fields only yielded slight improvements in forecasting certain fields at longer lead times. The results also suggest that a smaller number of input time steps or smaller number of autoregressive steps can achieve better prediction skills, while also improving the overall computational efficiency. This research offers valuable insights into the strengths and weaknesses of different DL techniques for AR forecasting, hopefully guiding the development of improved models for forecasting this phenomenon.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Development of message passing-based graph convolutional networks for classifying cancer pathology reports

Abstract Background Applying graph convolutional networks (GCN) to the classification of free-form natural language texts leveraged by graph-of-words features (TextGCN) was studied and confirmed to be an effective means of describing complex natural language texts. However, the text classification models based on the TextGCN possess weaknesses in terms of memory consumption and model dissemination and distribution. In this paper, we present a fast message passing network (FastMPN), implementing a GCN with message passing architecture that provides versatility and flexibility by allowing trainable node embedding and edge weights, helping the GCN model find the better solution. We applied the FastMPN model to the task of clinical information extraction from cancer pathology reports, extracting the following six properties: main site, subsite, laterality, histology, behavior, and grade. Results We evaluated the clinical task performance of the FastMPN models in terms of micro- and macro-averaged F1 scores. A comparison was performed with the multi-task convolutional neural network (MT-CNN) model. Results show that the FastMPN model is equivalent to or better than the MT-CNN. Conclusions Our implementation revealed that our FastMPN model, which is based on the PyTorch platform, can train a large corpus (667,290 training samples) with 202,373 unique words in less than 3 minutes per epoch using one NVIDIA V100 hardware accelerator. Our experiments demonstrated that using this implementation, the clinical task performance scores of information extraction related to tumors from cancer pathology reports were highly competitive.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Improved Subseasonal Forecasting of Extreme Polar Vortices Using Machine Learning

Our research was focused on forecasting the position and shape of the winter stratospheric polar vortex at a subseasonal timescale of 15 days in advance. To achieve this, we employed both statistical and neural network machine learning techniques. The analysis was performed on 42 winter seasons of reanalysis data provided by NASA giving us a total of 6,342 days of data. The state of the polar vortex for determined by using geometric moments to calculate the centroid latitude and the aspect ratio of an ellipse fit onto the vortex. Timeseries for thirty additional precursors were calculated to help improve the predictive capabilities of the algorithm. Feature importance of these precursors was performed using random forest to measure the predictive importance and the ideal number of precursors. Then, using the precursors identified as important, various statistical methods were tested for predictive accuracy with random forest and nearest neighbor performing the best. An echo state network, a type of recurrent neural network that features sparsely connected hidden layer and a reduced number of trainable parameters that allows for rapid training and testing, was also implemented for the forecasting problem. Hyperparameter tuning was performed for each methods using a subset of the training data. The algorithms were trained and tuned on the first 41 years of data, then tested for accuracy on the final year. In general, the centroid latitude of the polar vortex proved easier to predict than the aspect ratio across all algorithms. Random forest outperformed other statistical forecasting algorithms overall but struggled to predict extreme values. Forecasting from echo state network suggested a strong predictive capability past 15 days, but further work is required to fully realize the potential of recurrent neural network approaches.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗
DOE OSTI2024

Continuous integration data-driven platform of industrial-scale subsurface storage for real-time analytics

This project helped address the growing need for efficient and scalable models to support geological carbon and energy storage, which are crucial for achieving net-zero emissions. Traditionally accurate high-fidelity numerical models have been used to simulate relevant storage processes under a handful of processes, however such models are computationally demanding, making uncertainty quantification impractical. Consequently, we first developed a machine learning framework, based on Graph Neural Operators (GNOs), to improving the accuracy of model predictions for a fixed computational budget. We then developed an Ensemble of Improved Neural Operators (ENO), which uses bagging and Monte Carlo dropout techniques, to further improve prediction accuracy. Lastly, we developed the way to explain progressive transfer learning methods to reduce the amount of training data and computational cost of training (i.e., reduce trainable parameters) when using our models for multiple storage sites. Our numerical investigation, which used real-world case studies, demonstrated that our framework can significantly improve the safety and efficiency of geological storage operations, with potential applications in other domains such as geothermal reservoirs and climate modeling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Unrolled Video Super-Resolution Network with Autoregressive Prior for the Case of Known Motion

Real-time detection and classification of distant objects is necessary for many national security applications. However, when objects are far from the sensor, they occupy only a small number of pixels in the captured video, limiting the amount of visual detail available for recognition. State-of-the-art classification methods typically rely on high-resolution (HR) video streams to capture characteristic object features, but obtaining such detail is challenging for distant objects that occupy only a few pixels. This motivates the development of video super-resolution (VSR) methods that enhance object classification by recovering fine details from low-pixel representations. Current VSR methods rely either on model-based optimization, which is interpretable but computationally expensive, or on learning-based approaches, which are efficient and high-performing but often lack flexibility and interpretability. In this report, we propose an end-to-end trainable unrolled VSR network, UVSRNet, which super-resolves each frame in a video by exploiting sub-pixel motion between neighboring low-resolution (LR) frames as well as incorporating high-frequency detail from previously super-resolved frames. In particular, by unrolling a plug-and-play (PnP) half-quadratic splitting (HQS) algorithm, we leverage a model-based data-fitting module alongside a learning-based autoregressive prior module. This combination yields a method that maintains the flexibility and interpretability of model-based methods while achieving the performance advantages of learning-based methods.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2025

CRCNS22 Learning Rules in the Hippocampus and their Mapping to Neuromorphic Systems (Final Technical Report)

Large scale biologically-realistic computational models are key to investigating the interplay between structure and function in nervous systems, thus paving the way to new clinical methods and neuro-inspired computing solutions. This project focuses on the hippocampus, in particular the CA3-CA1 regions, due to their role in associative learning and memory, pattern separation and completion, and spatial navigation. Investigations into the neuronal organization and learning rule(s) of this circuit can shed light into how declarative memories are formed, stored, recalled and forgotten and inform computational, experimental and clinical neuroscience work. Our project aims at developing a novel data-driven methodology supported by a broad heterogeneous base of neuroscience experimental knowledge and inspired from advances in computer science and engineering. Specifically, this work will benchmark existing and new learning rules within a full-scale spiking neural network simulation of the CA3-CA1 region. The model will be based on an open-source repository, called the Hippocampome, which contains neuronal morphologies, firing patterns, synapse probabilities, and most other required parameters for all known neuron types in the rodent hippocampal formation. The model will be first trained in a supervised fashion for associative memory tasks using backpropagation through time traditionally used in computer science, enhanced with a new technique called the surrogate gradient method. This optimization method will be used to obtain a global loss minimization, but it is not biologically inspired as it assumes the use of data not locally available to the synapses. However, we propose its use as a benchmarking tool, to compare the training performance of local biologically plausible and hardware-mappable learning rules at scale. New rules or combinations will be proposed and tested as needed, based on the obtained results. Progress in this area will also drive the development of novel hardware-mappable algorithms for continual lifelong learning and categorization of new events from few presented examples. This project goes beyond the existing state-of-the-art by looking at large scale realistic neuronal circuits as networks trainable via global optimization methods such as surrogate gradient descent. The objective function of the brain that supports learning is largely unknown, but it is likely that it operates through local learning rules. Studying network trajectories around local minima as proposed in this work represents a useful strategy for understanding whether a network is training by using a specific (set of) learning rule(s). Starting from a completely untrained network is a challenging test since it is difficult to determine how the learning rule affects the trajectory of the network. This interdisciplinary project will help understand what rule governs learning in these regions or if multiple learning rules are involved. The work will develop a robust methodology to measure if the network is converging to the target solution, oscillating around it, or diverging away.

59 BASIC BIOLOGICAL SCIENCES↗