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At least 919 records · Page 51

A Barrier-Certificated Reinforcement Learning Approach for Enhancing Power System Transient Stability

Increasing integration of renewable resources brings more flexibility and poses new challenges to modern power systems, leading to highly nonlinear and complex dynamics. Here, this paper aims to provide a general solution framework to traditional control problems, such as frequency control and voltage control, which attempt to maintain the stability of either synchronous generators-governed or inverter-governed systems when subjected to a disturbance and simultaneously guarantee operational constraints, providing a complete complement to existing works on control design. Building on reinforcement learning (RL) and control barrier functions, the framework includes two subsystems, i.e., a model-free controller and a barrier-certification system, which discover RL-based control actions and sequentially filter them using a barrier certificate to satisfy operational constraints. Calculating a barrier function is generally challenging for a complex power system. This is addressed by representing the barrier function using neural networks (NNs) and data-based approaches. An adaptive method is introduced to certify the neural barrier function that perseveres barrier conditions, which is more compatible with online implementation. The proposed framework synthesizes a stabilizing controller that satisfies predefined safety regions. The effectiveness of the proposed framework is demonstrated via several comparative case studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Proteomic assessment of serum biomarkers of longevity in older men

The biological bases of longevity are not well understood, and there are limited biomarkers for the prediction of long life. We used a high-throughput, discovery-based proteomics approach to identify serum peptides and proteins that were associated with the attainment of longevity in a longitudinal study of community-dwelling men age ≥65 years. Baseline serum in 1196 men were analyzed using liquid chromatography–ion mobility–mass spectrometry, and lifespan was determined during ~12 years of follow-up. Men who achieved longevity (≥90% expected survival) were compared to those who died earlier. Rigorous statistical methods that controlled for false positivity were utilized to identify 25 proteins that were associated with longevity. All these proteins were in lower abundance in long-lived men and included a variety involved in inflammation or complement activation. Lower levels of longevity-associated proteins were also associated with better health status, but as time to death shortened, levels of these proteins increased. Pathway analyses implicated a number of compounds as important upstream regulators of the proteins and implicated shared networks that underlie the observed associations with longevity. Overall, these results suggest that complex pathways, prominently including inflammation, are linked to the likelihood of attaining longevity. This work may serve to identify novel biomarkers for longevity and to understand the biology underlying lifespan.

60 APPLIED LIFE SCIENCES↗

Bayesian homodyne and heterodyne tomography

Continuous-variable (CV) photonic states are of increasing interest in quantum information science, bolstered by features such as deterministic resource state generation and error correction via bosonic codes. Data-efficient characterization methods will prove critical in the fine-tuning and maturation of such CV quantum technology. Although Bayesian inference offers appealing properties—including uncertainty quantification and optimality in mean-squared error—Bayesian methods have yet to be demonstrated for the tomography of arbitrary CV states. Here we introduce a complete Bayesian quantum state tomography workflow capable of inferring generic CV states measured by homodyne or heterodyne detection, with no assumption of Gaussianity. As examples, we demonstrate our approach on experimental coherent, thermal, and cat state data, obtaining excellent agreement between our Bayesian estimates and theoretical predictions. Our approach lays the groundwork for Bayesian estimation of highly complex CV quantum states in emerging quantum photonic platforms, such as quantum communications networks and sensors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

3-D Geologic Controls of Hydrothermal Fluid Flow at Brady Geothermal Field, Nevada using PCA

In many hydrothermal systems, fracture permeability along faults provides pathways for groundwater to transport heat from depth. Faulting generates a range of deformation styles that cross-cut heterogeneous geology, resulting in complex patterns of permeability, porosity, and hydraulic conductivity. Vertical connectivity (a through going network of permeable areas that allows advection of heat from depth to the shallow subsurface) is rare and is confined to relatively small volumes that have highly variable spatial distribution. This local compartmentalization of connectivity represents a significant challenge to understanding hydrothermal circulation and for exploring, developing, and managing hydrothermal resources. Here, we present an evaluation of the geologic characteristics that control this compartmentalization in hydrothermal systems through 3-D analysis of the Brady geothermal field in western Nevada. A published 3-D geologic map of the Brady area is used as a basis to develop structural and geological variables that are hypothesized to control or effect permeability or connectivity. The 3-D distribution of these variables is compared to the distribution of productive and non-productive fluid flow intervals along production wells and non-productive wells via principal component analysis (PCA). This comparison elucidates which geologic and structural variables are most closely associated with productive fluid flow intervals. Results indicate that production intervals at Brady are located: (1) within or near to known and stress-loaded macro-scale faults, and (2) in areas of high fault and fracture density. This submission includes the published journal article detailing this work, the published 3-D geologic map of the Brady Geothermal Area used as a basis to develop structural and geological variables that are hypothesized to control or effect permeability or connectivity, 3-D well data, along which geologic data were sampled for PCA analyses, and associated metadata file. This work was done using existing R programs.

15 GEOTHERMAL ENERGY↗

AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Final Report)

The AGGREGATE project team successfully developed and validated various modules for outage management. Brief summaries of each module are provided to showcase their strength for outage management and restoration for a distribution system with a high penetration of connected distribution energy resources (DERs). In recent years, inverter-based DERs have been widely deployed in distribution system. A most of behind-the-meter (BTM) solar power generation is not visible to the utility. The data-driven DER and load estimation modules are using machine learning (ML) and artificial intelligence (AI) to manage this issue, which provides an opportunity for distribution system operators (DSOs) to operate systems and make decisions in real-time for a distribution system with a high penetration of DERs deployed. Also, the estimated DER and true load can be further leveraged in network aggregation and cold-load pick up estimation for reducing the computing complexity and providing for fast restoration. After load demand and DER power generations have been estimated, the information will support topology and state estimation (SE). The topology estimation module demonstrated the viability of mixed integer linear programming (MILP) formulation to estimate the most likely operational radial topology and outage sections using power flow measurements, historical/estimated load and DERs data and smart meter ping measurements. Formulation includes continuous (power flow, load and DERs data) and binary measurements (smart meter ping measurements) in a single formulation. Errors in continuous data and binary data are modeled as normal distribution and Bernoulli distribution, respectively. In the future distribution grid, the power injection from controllable DERs will be essential for efficient and resilient grid operation. However, determining the optimal DER injections and restoration actions is dependent on knowledge of the system states. State estimation (SE), already the cornerstone of transmission energy management systems, will become commonplace in distribution management systems as more measurements become available from deployment of automated metering infrastructure (AMI). Observability analysis is the first step in SE, as it determines the sufficiency of the available measurements for accurately estimating the current system states. A new type of pseudo-measurement called a Correlational Measurement (CM) is introduced in this module, to enhance the observability of the system to enable more accurate SE. CMs encapsulate knowledge of correlation between demand patterns for similar classes of loads as well as injection patterns for same-technology renewable DERs. During grid contingency scenarios, DERs have been traditionally disconnected, without any fault ride-through capabilities. However, with new regulations and better technology, it is feasible for these resources to contribute to the grid’s restoration after an adverse event and hence enhance resilience. The controllability module proposes a two-step restoration scheme for the power system restoration process by leveraging additional degrees of freedom in power electronics interfaced DERs for mitigating voltage problems. In a resilience mode without the utility system, the distribution grid relies on DERs to serve critical load. In such a severe event with multiple faults on the distribution feeders, actuation of various protective devices (PDs) divides the distribution system into electrical islands. The undetected actuated PDs due to fault current contributions from DERs can delay the restoration process, thereby reducing the system resilience. The Advanced Outage Management (AOM) and the Advanced Feeder Restoration (AFR) modules developed in this project provide improved system resilience with multiple DERs. AOM identifies the faulted sections and actuated PDs in a distribution system with DERs by incorporating smart meter data. The most credible outage scenario including fault locations, PD actuations, and fault indicator (FI) failures is identified by a set of binary integer linear programming incorporating hypotheses. The AFR module serves to restore a distribution system with available energy resources taking into consideration the availability of utility sources and DERs. By partitioning the system into islands, critical load will be served with the available generation resources within islands based on the solution of a MILP. When the utility systems become available, the optimal path will be determined by a spanning tree search algorithm that reconnects these islands back to substations and restores the remaining load. The transmission and distribution (T&D) co-simulation module was used to validate the effect of a control action performed on the distribution side assets as it propagates to the transmission side. This ensures that the control action performed results in a feasible operating point on both the transmission and the distribution system. In addition to validation, the team used the T&D co-simulation module to demonstrate how distribution system assets can be used to mitigate issues on the transmission system. Specifically, the team demonstrated that appropriate switching operations on the distribution side can alleviate the line overload condition on the transmission side without causing new operational constraint violations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Protein-ligand binding affinity prediction using multi-instance learning with docking structures

Recent advances in 3D structure-based deep learning approaches demonstrate improved accuracy in predicting protein-ligand binding affinity in drug discovery. These methods complement physics-based computational modeling such as molecular docking for virtual high-throughput screening. Despite recent advances and improved predictive performance, most methods in this category primarily rely on utilizing co-crystal complex structures and experimentally measured binding affinities as both input and output data for model training. Nevertheless, co-crystal complex structures are not readily available and the inaccurate predicted structures from molecular docking can degrade the accuracy of the machine learning methods. We introduce a novel structure-based inference method utilizing multiple molecular docking poses for each complex entity. Our proposed method employs multi-instance learning with an attention network to predict binding affinity from a collection of docking poses. We validate our method using multiple datasets, including PDBbind and compounds targeting the main protease of SARS-CoV-2. The results demonstrate that our method leveraging docking poses is competitive with other state-of-the-art inference models that depend on co-crystal structures. This method offers binding affinity prediction without requiring co-crystal structures, thereby increasing its applicability to protein targets lacking such data.

97 MATHEMATICS AND COMPUTING↗

Quantum-enhanced photoprotection in neuroprotein architectures emerges from collective light-matter interactions

Background Superradiance is the phenomenon of many identical quantum systems absorbing and/or emitting photons collectively at a higher rate than any one system can individually. This phenomenon has been studied analytically in idealized distributions of electronic two-level systems (TLSs), each with a ground and excited state, as well as numerically in realistic photosynthetic nanotubes and cytoskeletal architectures. Methods Superradiant effects are studied here in idealized toy model systems and realistic biological mega-networks of tryptophan (Trp) molecules, which are strongly fluorescent amino acids found in many proteins. Each Trp molecule acts as a chromophore absorbing in the ultraviolet spectrum and can be treated approximately as a TLS, with its 1 L a excited singlet state; thus, organized Trp networks can exhibit superradiance. Such networks are found, for example, in microtubules, actin filaments, and amyloid fibrils. Microtubules and actin filaments are spiral-cylindrical protein polymers that play significant biological roles as primary constituents of the eukaryotic cytoskeleton, while amyloid fibrils have been targeted in a variety of neurodegenerative diseases. We treat these proteinaceous Trp networks as open quantum systems, using a non-Hermitian Hamiltonian to describe interactions of the chromophore network with the electromagnetic field. We numerically diagonalize the Hamiltonian to obtain its complex eigenvalues, where the real part is the energy and the imaginary part is its associated enhancement rate. We also consider multiple realizations of increasing static disorder in either the site energies or the decay rates. Results We obtained the energies and enhancement rates for realistic microtubules, actin filament bundles, and amyloid fibrils of differing lengths, and we use these values to calculate the quantum yield, which is the ratio of the number of photons emitted to the number of photons absorbed. We find that all three of these structures exhibit highly superradiant states near the low-energy portion of the spectrum, which enhances the magnitude and robustness of the quantum yield to static disorder and thermal noise. Conclusion The high quantum yield and stable superradiant states in these biological architectures may play a photoprotective rolein vivo, downconverting energetic ultraviolet photons—absorbed from those emitted by reactive free radical species—to longer, safer wavelengths and thereby mitigating biochemical stress and photophysical damage. Contrary to conventional assumptions that quantum effects cannot survive in large biosystems at high temperatures, our results suggest that macropolymeric collectives of TLSs in microtubules, actin filaments, and amyloid fibrils exhibit increasingly observable and robust effects with increasing length, up to the micron scale, due to quantum coherent interactions in the single-photon limit. Superradiant enhancement and high quantum yield exhibited in neuroprotein polymers could thus play a crucial role in information processing in the brain, the development of neurodegenerative diseases such as Alzheimer’s and related dementias, and a wide array of other pathologies characterized by anomalous protein aggregates.

Physics↗

WHONDRS-GUI: a web application for global survey of surface water metabolites

Background The Worldwide Hydrobiogeochemistry Observation Network for Dynamic River Systems (WHONDRS) is a consortium that aims to understand complex hydrologic, biogeochemical, and microbial connections within river corridors experiencing perturbations such as dam operations, floods, and droughts. For one ongoing WHONDRS sampling campaign, surface water metabolite and microbiome samples are collected through a global survey to generate knowledge across diverse river corridors. Metabolomics analysis and a suite of geochemical analyses have been performed for collected samples through the Environmental Molecular Sciences Laboratory (EMSL). The obtained knowledge and data package inform mechanistic and data-driven models to enhance predictions of outcomes of hydrologic perturbations and watershed function, one of the most critical components in model-data integration. To support efforts of the multi-domain integration and make the ever-growing data package more accessible for researchers across the world, a Shiny/R Graphical User Interface (GUI) called WHONDRS-GUI was created. Results The web application can be run on any modern web browser without any programming or operational system requirements, thus providing an open, well-structured, discoverable dataset for WHONDRS. Together with a context-aware dynamic user interface, the WHONDRS-GUI has functionality for searching, compiling, integrating, visualizing and exporting different data types that can easily be used by the community. The web application and data package are available at https://data.ess-dive.lbl.gov/view/doi:10.15485/1484811 , which enables users to simultaneously obtain access to the data and code and to subsequently run the web app locally. The WHONDRS-GUI is also available for online use at Shiny Server ( https://xmlin.shinyapps.io/whondrs/ ).

59 BASIC BIOLOGICAL SCIENCES↗

Modeling Analog Tile-Based Accelerators Using SST

Analog computing has been widely proposed to improve the energy efficiency of multiple important workloads including neural network operations, and other linear algebra kernels. To properly evaluate analog computing and explore more complex workloads such as systems consisting of multiple analog data paths, system level simulations are required. Moreover, prior work on system architectures for analog computing often rely on custom simulators creating signficant additional design effort and complicating comparisons between different systems. To remedy these issues, this report describes the design and implementation of a flexible tile-based analog accelerator element for the Structural Simulation Toolkit (SST). The element focuses on heavily on the tile controller—an often neglected aspect of prior work—that is sufficiently versatile to simulate a wide range of different tile operations including neural network layers, signal processing kernels, and generic linear algebra operations without major constraints. The tile model also interoperates with existing SST memory and network models to reduce the overall development load and enable future simulation of heterogeneous systems with both conventional digital logic and analog compute tiles. Finally, both the tile and array models are designed to easily support future extensions as new analog operations and applications that can benefit from analog computing are developed.

97 MATHEMATICS AND COMPUTING↗

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

58 GEOSCIENCES↗

Toward Quantifying Vulnerabilities in Critical Infrastructure Systems

Modern society is increasingly dependent on the stability of a complex system of interdependent infrastructure sectors. Vulnerability in critical infrastructures (CIs) is defined as a measure of system susceptibility to threat scenarios. Quantifying vulnerability in CIs has not been adequately addressed in the literature. This paper presents ongoing research on how the authors model CIs as network-based models and propose a set of metrics to quantify vulnerability in CI systems. The size and complexity of the CIs make this a challenging task. These metrics could be used for planning and efficient decision-making during extreme events.

Devineni, Pravallika↗

Self-consistent hopping theory of activated relaxation and diffusion of dilute penetrants in dense crosslinked polymer networks

We generalize a microscopic statistical mechanical theory of the activated dynamics of dilute spherical penetrants in glass-forming liquids to study the influence of crosslinking in polymer networks on the penetrant relaxation time and diffusivity over a wide range of temperature and crosslink fraction (f n ). Our calculations are relevant to recent experimental studies of a nm-sized molecule diffusing in poly-(n-butyl methacrylate) networks. The theory predicts the penetrant relaxation time increases exponentially with the glass transition temperature, T g (f n ), which grows roughly linearly with the square root of fn due to the coupling of local hopping to longer-range collective elasticity. Moreover, T g is also found to be proportional to a geometric confinement parameter defined as the ratio of the penetrant diameter to the mean network mesh size. The decoupling ratio of the penetrant and Kuhn segment alpha times displays a complex non-monotonic dependence on f n and temperature that is well collapsed based on the variable T g (f n )/T. A model for the penetrant diffusion constant that combines activated relaxation and entropic mesh confinement is proposed, which results in a significantly stronger suppression of mass transport with degree of effective supercooling than predicted for the penetrant alpha time. Furthermore, this behavior corresponds to a new network-based type of “decoupling” of diffusion and relaxation. In contrast to the diffusion of larger nanoparticles in high temperature rubbery networks, our analysis in the supercooled regime suggests that for the penetrants studied the mesh confinement effects are of secondary importance relative to the consequences of crosslink-induced slowing down of activated hopping of glassy physics origin.

Chemistry↗

Exascale granular microstructure reconstruction in 3D volumes of arbitrary geometries with generative learning

Reconstructing 3D granular microstructures within volumes of arbitrary geometries from limited 2D image data is crucial for predicting the material properties, as well as performances of structural components accounting for material microstructural effects. We present a novel generative learning framework that enables exascale reconstruction of granular microstructures within complex 3D geometric volumes. Building upon existing transfer learning techniques using pre-trained convolutional neural networks (CNN), we introduce several key innovations to overcome the difficulties inherent in arbitrary geometries. Our framework incorporates periodic boundary conditions using circular padding techniques, ensuring continuity and representativeness of the reconstructed microstructures. We also introduce a novel seamless transition reconstruction (STR) method that creates statistically equivalent transition zones to integrate multiple pre-existing 3D microstructure volumes. Based on STR, we propose a cost-effective strategy for reconstructing microstructures within complex geometric volumes, minimizing computational waste. Validation through numerical experiments using kinetic Monte Carlo simulations demonstrates accurate reproduction of grain statistics, including grain size distributions and morphology. A case study involving the reconstruction of a 4-blade propeller microstructure illustrates the method’s capability to efficiently handle complex geometries. In conclusion, the proposed framework significantly reduces computational demands while maintaining high reconstruction quality, paving the way for scalable microstructure reconstruction in materials design and analysis.

36 MATERIALS SCIENCE↗

Multi-Level Structural Damage Characterization Using Sparse Acoustic Sensor Networks and Knowledge Transferred Deep Learning

Standard structural health monitoring techniques face well-known difficulties for comprehensive defect diagnosis in real-world structures that have structural, material, or geometric complexity. This motivates the exploration of machine-learning-based structural health monitoring methods in complex structures. However, creating sufficient training data sets with various defects is an ongoing challenge for data-driven machine (deep) learning algorithms. The ability to transfer the knowledge of a trained neural network from one component to another or to other sections of the same component would drastically reduce the required training data set. Also, it would facilitate computationally inexpensive machine learning based inspection systems. In this work, a machine-learning-based multi-level damage characterization is demonstrated with the ability to transfer trained knowledge within the sparse sensor network. A novel network spatial assistance and an adaptive convolution technique are proposed for efficient knowledge transfer within the deep learning algorithm. Proposed structural health monitoring method is experimentally evaluated on an aluminum plate with artificially induced defects. It was observed that the method improves the performance of knowledge transferred damage characterization by 50% during localization and 24% during severity assessment. Further, experiments using time windows with and without multiple edge reflections are studied. Results reveal that multiply scattered waves contain rich and deterministic defect signatures that can be mined using deep learning neural networks, improving the accuracy of both identification and quantification. In the case of a fixed sensor network, using multiply scattered waves shows 100% prediction accuracy at all levels of damage characterization.

36 MATERIALS SCIENCE↗

Minimization of Disorder as a Key Design Principle for Natural Sizes of Light Harvesting 2 Complexes

The light harvesting 2 (LH2) complex of purple bacteria has excellent energy conversion efficiency. Clarifying the design principle behind such efficiency at the atomistic level is crucial for understanding its structure–function relationship and can be utilized for the design of artificial light harvesting systems. To this end, we conducted comprehensive computational investigation of the dynamical and statistical nature of electronic excited states of pigment molecules in a natural LH2 complex with 9-fold symmetry and its two non-natural in silico analogues with 6- and 12-fold symmetries. To ensure reliable and efficient all-atomistic molecular dynamics simulations, we combined a well established interpolation approach for the construction of the potential energy surface with a neural network machine learning approach. Outcomes of these calculations clarify that non-natural forms of LH2-type complexes have significantly larger quasistatic disorder than those for the natural one. In addition, non-natural systems have more disruptions of the hydrogen bonding, underscoring its crucial role for reducing the disorder. On the other hand, local environmental dynamics are relatively insensitive to the structural changes although there is moderate enhancement in the anharmonic or interatomic components for the synthetic ones. These findings based on all-atomistic simulations provide direct computational evidence that the structure and sizes of natural LH2 complexes are designed to minimize the energetic disorder. We analyze quantitative implications of these for the energy transferring capability of the LH2 complex.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Abstract Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Prediction of plant complex traits via integration of multi-omics data

The formation of complex traits is the consequence of genotype and activities at multiple molecular levels. However, connecting genotypes and these activities to complex traits remains challenging. Here, we investigate whether integrating genomic, transcriptomic, and methylomic data can improve prediction for six Arabidopsis traits. We find that transcriptome- and methylome-based models have performances comparable to those of genome-based models. However, models built for flowering time using different omics data identify different benchmark genes. Nine additional genes identified as important for flowering time from our models are experimentally validated as regulating flowering. Gene contributions to flowering time prediction are accession-dependent and distinct genes contribute to trait prediction in different genotypes. Models integrating multi-omics data perform best and reveal known and additional gene interactions, extending knowledge about existing regulatory networks underlying flowering time determination. These results demonstrate the feasibility of revealing molecular mechanisms underlying complex traits through multi-omics data integration.

59 BASIC BIOLOGICAL SCIENCES↗

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗