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Title: Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles
Physics-based models are often used to study engineering and environmental systems. The ability to model these systems is the key to achieving our future environmental sustainability and improving the quality of human life. This article focuses on simulating lake water temperature, which is critical for understanding the impact of changing climate on aquatic ecosystems and assisting in aquatic resource management decisions. General Lake Model (GLM) is a state-of-the-art physics-based model used for addressing such problems. However, like other physics-based models used for studying scientific and engineering systems, it has several well-known limitations due to simplified representations of the physical processes being modeled or challenges in selecting appropriate parameters. While state-of-the-art machine learning models can sometimes outperform physics-based models given ample amount of training data, they can produce results that are physically inconsistent. This article proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improves the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physics-based models (by over 20% even with very little training data), while generating outputs consistent with physical laws. An important aspect of our PGRNN approach lies in more » its ability to incorporate the knowledge encoded in physics-based models. This allows training the PGRNN model using very few true observed data while also ensuring high prediction accuracy. Although we present and evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where physics-based (also known as mechanistic) models are used. « less
Authors:
; ; ; ; ; ;
Award ID(s):
1934721
Publication Date:
NSF-PAR ID:
10287165
Journal Name:
ACM/IMS Transactions on Data Science
Volume:
2
Issue:
3
Page Range or eLocation-ID:
1 to 26
ISSN:
2691-1922
Sponsoring Org:
National Science Foundation
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  1. This paper proposes a physics-guided recurrent neural network model (PGRNN) that combines RNNs and physics-based models to leverage their complementary strengths and improve the modeling of physical processes. Specifically, we show that a PGRNN can improve prediction accuracy over that of physical models, while generating outputs consistent with physical laws, and achieving good generalizability. Standard RNNs, even when producing superior prediction accuracy, often produce physically inconsistent results and lack generalizability. We further enhance this approach by using a pre-training method that leverages the simulated data from a physics-based model to address the scarcity of observed data. Although we present andmore »evaluate this methodology in the context of modeling the dynamics of temperature in lakes, it is applicable more widely to a range of scientific and engineering disciplines where mechanistic (also known as process-based) models are used, e.g., power engineering, climate science, materials science, computational chemistry, and biomedicine.« less
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  3. Obeid, I. (Ed.)
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It is well known that state of the art algorithms in machine learning require vast amounts of data. Fields such as speech recognition [3], image recognition [4] and text processing [5] are able to deliver impressive performance with complex deep learning models because they have developed large corpora to support training of extremely high-dimensional models (e.g., billions of parameters). Other fields that do not have access to such data resources must rely on techniques in which existing models can be adapted to new datasets [6]. A preliminary version of this breast corpus release was tested in a pilot study using a baseline machine learning system, ResNet18 [7], that leverages several open-source Python tools. The pilot corpus was divided into three sets: train, development, and evaluation. Portions of these slides were manually annotated [1] using the nine labels in Table 1 [8] to identify five to ten examples of pathological features on each slide. Not every pathological feature is annotated, meaning excluded areas can include focuses particular to these labels that are not used for training. A summary of the number of patches within each label is given in Table 2. To maintain a balanced training set, 1,000 patches of each label were used to train the machine learning model. Throughout all sets, only annotated patches were involved in model development. The performance of this model in identifying all the patches in the evaluation set can be seen in the confusion matrix of classification accuracy in Table 3. The highest performing labels were background, 97% correct identification, and artifact, 76% correct identification. A correlation exists between labels with more than 6,000 development patches and accurate performance on the evaluation set. Additionally, these results indicated a need to further refine the annotation of invasive ductal carcinoma (“indc”), inflammation (“infl”), nonneoplastic features (“nneo”), normal (“norm”) and suspicious (“susp”). This pilot experiment motivated changes to the corpus that will be discussed in detail in this poster presentation. To increase the accuracy of the machine learning model, we modified how we addressed underperforming labels. One common source of error arose with how non-background labels were converted into patches. Large areas of background within other labels were isolated within a patch resulting in connective tissue misrepresenting a non-background label. In response, the annotation overlay margins were revised to exclude benign connective tissue in non-background labels. Corresponding patient reports and supporting immunohistochemical stains further guided annotation reviews. The microscopic diagnoses given by the primary pathologist in these reports detail the pathological findings within each tissue site, but not within each specific slide. The microscopic diagnoses informed revisions specifically targeting annotated regions classified as cancerous, ensuring that the labels “indc” and “dcis” were used only in situations where a micropathologist diagnosed it as such. Further differentiation of cancerous and precancerous labels, as well as the location of their focus on a slide, could be accomplished with supplemental immunohistochemically (IHC) stained slides. When distinguishing whether a focus is a nonneoplastic feature versus a cancerous growth, pathologists employ antigen targeting stains to the tissue in question to confirm the diagnosis. For example, a nonneoplastic feature of usual ductal hyperplasia will display diffuse staining for cytokeratin 5 (CK5) and no diffuse staining for estrogen receptor (ER), while a cancerous growth of ductal carcinoma in situ will have negative or focally positive staining for CK5 and diffuse staining for ER [9]. Many tissue samples contain cancerous and non-cancerous features with morphological overlaps that cause variability between annotators. The informative fields IHC slides provide could play an integral role in machine model pathology diagnostics. Following the revisions made on all the annotations, a second experiment was run using ResNet18. Compared to the pilot study, an increase of model prediction accuracy was seen for the labels indc, infl, nneo, norm, and null. This increase is correlated with an increase in annotated area and annotation accuracy. Model performance in identifying the suspicious label decreased by 25% due to the decrease of 57% in the total annotated area described by this label. A summary of the model performance is given in Table 4, which shows the new prediction accuracy and the absolute change in error rate compared to Table 3. The breast tissue subset we are developing includes 3,505 annotated breast pathology slides from 296 patients. The average size of a scanned SVS file is 363 MB. The annotations are stored in an XML format. A CSV version of the annotation file is also available which provides a flat, or simple, annotation that is easy for machine learning researchers to access and interface to their systems. Each patient is identified by an anonymized medical reference number. Within each patient’s directory, one or more sessions are identified, also anonymized to the first of the month in which the sample was taken. These sessions are broken into groupings of tissue taken on that date (in this case, breast tissue). A deidentified patient report stored as a flat text file is also available. Within these slides there are a total of 16,971 total annotated regions with an average of 4.84 annotations per slide. Among those annotations, 8,035 are non-cancerous (normal, background, null, and artifact,) 6,222 are carcinogenic signs (inflammation, nonneoplastic and suspicious,) and 2,714 are cancerous labels (ductal carcinoma in situ and invasive ductal carcinoma in situ.) The individual patients are split up into three sets: train, development, and evaluation. Of the 74 cancerous patients, 20 were allotted for both the development and evaluation sets, while the remain 34 were allotted for train. The remaining 222 patients were split up to preserve the overall distribution of labels within the corpus. This was done in hope of creating control sets for comparable studies. Overall, the development and evaluation sets each have 80 patients, while the training set has 136 patients. In a related component of this project, slides from the Fox Chase Cancer Center (FCCC) Biosample Repository (https://www.foxchase.org/research/facilities/genetic-research-facilities/biosample-repository -facility) are being digitized in addition to slides provided by Temple University Hospital. This data includes 18 different types of tissue including approximately 38.5% urinary tissue and 16.5% gynecological tissue. These slides and the metadata provided with them are already anonymized and include diagnoses in a spreadsheet with sample and patient ID. We plan to release over 13,000 unannotated slides from the FCCC Corpus simultaneously with v1.0.0 of TUDP. Details of this release will also be discussed in this poster. Few digitally annotated databases of pathology samples like TUDP exist due to the extensive data collection and processing required. The breast corpus subset should be released by November 2021. By December 2021 we should also release the unannotated FCCC data. We are currently annotating urinary tract data as well. We expect to release about 5,600 processed TUH slides in this subset. We have an additional 53,000 unprocessed TUH slides digitized. Corpora of this size will stimulate the development of a new generation of deep learning technology. In clinical settings where resources are limited, an assistive diagnoses model could support pathologists’ workload and even help prioritize suspected cancerous cases. ACKNOWLEDGMENTS This material is supported by the National Science Foundation under grants nos. CNS-1726188 and 1925494. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. REFERENCES [1] N. Shawki et al., “The Temple University Digital Pathology Corpus,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York City, New York, USA: Springer, 2020, pp. 67 104. https://www.springer.com/gp/book/9783030368432. [2] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning.” Major Research Instrumentation (MRI), Division of Computer and Network Systems, Award No. 1726188, January 1, 2018 – December 31, 2021. https://www. isip.piconepress.com/projects/nsf_dpath/. [3] A. Gulati et al., “Conformer: Convolution-augmented Transformer for Speech Recognition,” in Proceedings of the Annual Conference of the International Speech Communication Association (INTERSPEECH), 2020, pp. 5036-5040. https://doi.org/10.21437/interspeech.2020-3015. [4] C.-J. Wu et al., “Machine Learning at Facebook: Understanding Inference at the Edge,” in Proceedings of the IEEE International Symposium on High Performance Computer Architecture (HPCA), 2019, pp. 331–344. https://ieeexplore.ieee.org/document/8675201. [5] I. Caswell and B. Liang, “Recent Advances in Google Translate,” Google AI Blog: The latest from Google Research, 2020. [Online]. Available: https://ai.googleblog.com/2020/06/recent-advances-in-google-translate.html. [Accessed: 01-Aug-2021]. [6] V. Khalkhali, N. Shawki, V. Shah, M. Golmohammadi, I. Obeid, and J. Picone, “Low Latency Real-Time Seizure Detection Using Transfer Deep Learning,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2021, pp. 1 7. https://www.isip. piconepress.com/publications/conference_proceedings/2021/ieee_spmb/eeg_transfer_learning/. [7] J. Picone, T. Farkas, I. Obeid, and Y. Persidsky, “MRI: High Performance Digital Pathology Using Big Data and Machine Learning,” Philadelphia, Pennsylvania, USA, 2020. https://www.isip.piconepress.com/publications/reports/2020/nsf/mri_dpath/. [8] I. Hunt, S. Husain, J. Simons, I. Obeid, and J. Picone, “Recent Advances in the Temple University Digital Pathology Corpus,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2019, pp. 1–4. https://ieeexplore.ieee.org/document/9037859. [9] A. P. Martinez, C. Cohen, K. Z. Hanley, and X. (Bill) Li, “Estrogen Receptor and Cytokeratin 5 Are Reliable Markers to Separate Usual Ductal Hyperplasia From Atypical Ductal Hyperplasia and Low-Grade Ductal Carcinoma In Situ,” Arch. Pathol. Lab. Med., vol. 140, no. 7, pp. 686–689, Apr. 2016. https://doi.org/10.5858/arpa.2015-0238-OA.« less
  4. Green Lake is the deepest natural inland lake in Wisconsin, with a maximum depth of about 72 meters. In the early 1900s, the lake was believed to have very good water quality (low nutrient concentrations and good water clarity) with low dissolved oxygen (DO) concentrations occurring in only the deepest part of the lake. Because of increased phosphorus (P) inputs from anthropogenic activities in its watershed, total phosphorus (TP) concentrations in the lake have increased; these changes have led to increased algal production and low DO concentrations not only in the deepest areas but also in the middle of themore »water column (metalimnion). The U.S. Geological Survey has routinely monitored the lake since 2004 and its tributaries since 1988. Results from this monitoring led the Wisconsin Department of Natural Resources (WDNR) to list the lake as impaired because of low DO concentrations in the metalimnion, and they identified elevated TP concentrations as the cause of impairment. As part of this study by the U.S. Geological Survey, in cooperation with the Green Lake Sanitary District, the lake and its tributaries were comprehensively sampled in 2017–18 to augment ongoing monitoring that would further describe the low DO concentrations in the lake (especially in the metalimnion). Empirical and process-driven water-quality models were then used to determine the causes of the low DO concentrations and the magnitudes of P-load reductions needed to improve the water quality of the lake enough to meet multiple water-quality goals, including the WDNR’s criteria for TP and DO. Data from previous studies showed that DO concentrations in the metalimnion decreased slightly as summer progressed in the early 1900s but, since the late 1970s, have typically dropped below 5 milligrams per liter (mg/L), which is the WDNR criterion for impairment. During 2014–18 (the baseline period for this study), the near-surface geometric mean TP concentration during June–September in the east side of the lake was 0.020 mg/L and in the west side was 0.016 mg/L (both were above the 0.015-mg/L WDNR criterion for the lake), and the metalimnetic DO minimum concentrations (MOMs) measured in August ranged from 1.0 to 4.7 mg/L. The degradation in water quality was assumed to have been caused by excessive P inputs to the lake; therefore, the TP inputs to the lake were estimated. The mean annual external P load during 2014–18 was estimated to be 8,980 kilograms per year (kg/yr), of which monitored and unmonitored tributary inputs contributed 84 percent, atmospheric inputs contributed 8 percent, waterfowl contributed 7 percent, and septic systems contributed 1 percent. During fall turnover, internal sediment recycling contributed an additional 7,040 kilograms that increased TP concentrations in shallow areas of the lake by about 0.020 mg/L. The elevated TP concentrations then persisted until the following spring. On an annual basis, however, there was a net deposition of P to the bottom sediments. Empirical models were used to describe how the near-surface water quality of Green Lake would be expected to respond to changes in external P loading. Predictions from the models showed a relatively linear response between P loading and TP and chlorophyll-a (Chl-a) concentrations in the lake, with the changes in TP and Chl-a concentrations being less on a percentage basis (50–60 percent for TP and 30–70 percent for Chl-a) than the changes in P loading. Mean summer water clarity, quantified by Secchi disk depths, had a greater response to decreases in P loading than to increases in P loading. Based on these relations, external P loading to the lake would need to be decreased from 8,980 kg/yr to about 5,460 kg/yr for the geometric mean June–September TP concentration in the east side of the lake, with higher TP concentrations than in the west side, to reach the WDNR criterion of 0.015 mg/L. This reduction of 3,520 kg/yr is equivalent to a 46-percent reduction in the potentially controllable external P sources (all external sources except for precipitation, atmospheric deposition, and waterfowl) from those measured during water years 2014–18. The total external P loading would need to decrease to 7,680 kg/yr (a 17-percent reduction in potentially controllable external P sources) for near-surface June–September TP concentrations in the west side of the lake to reach 0.015 mg/L. Total external P loading would need to decrease to 3,870–5,320 kg/yr for the lake to be classified as oligotrophic, with a near-surface June–September TP concentration of 0.012 mg/L. Results from the hydrodynamic water-quality model GLM–AED (General Lake Model coupled to the Aquatic Ecodynamics modeling library) indicated that MOMs are driven by external P loading and internal sediment recycling that lead to high TP concentrations during spring and early summer, which in turn lead to high phytoplankton production, high metabolism and respiration, and ultimately DO consumption in the upper, warmer areas of the metalimnion. GLM–AED results indicated that settling of organic material during summer might be slowed by the colder, denser, and more viscous water in the metalimnion and thus increase DO consumption. Based on empirical evidence from a comparison of MOMs with various meteorological, hydrologic, water quality, and in-lake physical factors, MOMs were lower during summers, when metalimnetic water temperatures were warmer, near-surface Chl-a and TP concentrations were higher, and Secchi depths were lower. GLM–AED results indicated that the external P load would need to be reduced to about 4,060 kg/yr, a 57-percent reduction from that measured in 2014–18, to eliminate the occurrence of MOMs less than 5 mg/L during more than 75 percent of the years (the target provided by the WDNR). Large reductions in external P loading are expected to have an immediate effect on the near-surface TP concentrations and metalimnetic DO concentrations in Green Lake; however, it may take several years for the full effects of the external-load reduction to be observed because internal sediment recycling is an important source of P for the following spring.« less
  5. Demeniconi, Carlotta ; Davidson, Ian (Ed.)
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